Dot product, cross product, Newton's laws.

In summary, the conversation is about a student struggling in their Physics class and seeking help from a forum. They request guidance with their old homework assignments and are reminded to understand the concepts before attempting the problems. The conversation ends with the student being given a hint on how to add vectors and being encouraged to look up the definition of a vector.
  • #1
Neoriginal
12
0
My final for Physics is coming up and I really, really ****ed up in this class. I don't even know how to do dot products, cross products, or let alone Newton's laws. We applied Newton's laws to some pulley problems I think. I've been going to all the lectures but it just doesn't stick -- nothing seems to click. I found myself stumped on the midterm and I sat there like a complete dumb *** trying to look like I was writing something. After I miserably failed that final, I told myself I would get help wherever... I was thinking of this forum, and here I am now, one month later and a week before my final. I should have came sooner.

If you guys would, I could post some of my old homework assignments and you guys could help me work them out? I would appreciate it if someone did that. I know that some of you here are really into this stuff (and I want to also, but as of now I can't, being that I am completely lost), so I'm fairly confident that someone here could help me.

I know I completely ignored the format of this homework board, but it's in a .pdf file.

Thanks.
 
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  • #2
No replies?

:[

I've been reading over the intro chapters.. but it's still confusing (the book is "An Introduction to Mechanics" by Kleppner)
 
  • #3
You can post your old assignments, i think, but you will have to show how you worked them out.
It's according to the rules of the forum.(As for the book, I was suggested that Kleppner was a pretty high level and was directed to Halliday and Resnick...what grade are you in? )
 
  • #4
The legend said:
You can post your old assignments, i think, but you will have to show how you worked them out.
It's according to the rules of the forum.(As for the book, I was suggested that Kleppner was a pretty high level and was directed to Halliday and Resnick...what grade are you in? )

Freshman in college. There's no way I can work out the problems if I don't get the concepts. What I need help with is understanding the concepts. Only then can I begin to work out a problem.

That would be the equivalent of someone coming to me and asking if I can help them build a computer. My response to that would be, "first show me what you have done". Their response would be, "but I have no idea where to start"

That's just it, I have no idea where to start.'

First assignment: http://hep.ucsb.edu/courses/ph20/p1.pdf (About two months ago)

Page 49 of here you can find the problems that are listed as "KK 1.6", etc.

http://hep.ucsb.edu/courses/ph20/kkchap1.pdf

These problem sets are no longer worth points. This is in no way "cheating" since these assignments are long due. Do the same rules still apply that you can't simply "do" a problem for me. In fact, I'm not asking for you to "do" a problem for me. I'm asking for someone to "guide" me through the problem.
 
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  • #5
so you need help with all of these questions?
If there are just a few, just state the numbers...

I'll give a hint for the first.
By drawing what geometrical figure you can say that the sum of the given vectors is zero? Answering that, you should get your answer.
 
  • #6
The legend said:
so you need help with all of these questions?
If there are just a few, just state the numbers...

I'll give a hint for the first.
By drawing what geometrical figure you can say that the sum of the given vectors is zero? Answering that, you should get your answer.

A perpendicular line? <---.--->

Would that be a vector sum of zero?
 
  • #7
Neoriginal said:
What I need help with is understanding the concepts. Only then can I begin to work out a problem.
Then you need to ask about the specific concepts you need to understand better. You can do that e.g. in the classical physics forum.

Neoriginal said:
That would be the equivalent of someone coming to me and asking if I can help them build a computer. My response to that would be, "first show me what you have done". Their response would be, "but I have no idea where to start"

That's just it, I have no idea where to start.'
If you really have no idea, then it's OK to just say that. But you have to at least show us that you're not so lazy that you won't even bother to look up the definitions of the terms used in the problem you're asking about. So if you ask about vectors and have no idea where to start, you should at least post the definition of a vector.

Neoriginal said:
These problem sets are no longer worth points. This is in no way "cheating" since these assignments are long due. Do the same rules still apply that you can't simply "do" a problem for me. In fact, I'm not asking for you to "do" a problem for me. I'm asking for someone to "guide" me through the problem.
The rules still don't allow us to do the problems for you, but we can definitely guide you.

Neoriginal said:
First assignment: http://hep.ucsb.edu/courses/ph20/p1.pdf (About two months ago)

Page 49 of here you can find the problems that are listed as "KK 1.6", etc.

http://hep.ucsb.edu/courses/ph20/kkchap1.pdf
Do you really have no idea where to start with any of these? You should start with the definition of "vector". Tell us what definition you're using.
 
  • #8
Neoriginal said:
A perpendicular line? <---.--->

Would that be a vector sum of zero?
To add vectors in the form of "arrows", you need to move the arrow that represents the second vector so that it starts at the pointy end of the arrow that represents the first one. The sum is the arrow from the origin to the pointy end of that second arrow.

So yes, the sum of the two vectors you drew is zero. Now do it with vectors defined as ordered pairs of real numbers. What ordered pair is the zero vector? How is addition of ordered pairs defined? Can you find two ordered pairs that add up to the zero vector?
 
  • #9
Fredrik said:
Do you really have no idea where to start with any of these? You should start with the definition of "vector". Tell us what definition you're using.

This is straight from the textbook:

"From the geometric point of view, a vector is a directed line segment. In order to describe a vector we must specify both its length and direction. If two vectors have the same length and and the same direction they are equal."

Fredrik said:
To add vectors in the form of "arrows", you need to move the arrow that represents the second vector so that it starts at the pointy end of the arrow that represents the first one. The sum is the arrow from the origin to the pointy end of that second arrow.

Connect the tail of vector A to the head of vector B. I somewhat know about Ax, Ay, Az, Bx, By, Bz, and how it doesn't matter in what way you connect these vectors. But what I need help on are dot products and cross products (as mentioned in the title).

Fredrik said:
So yes, the sum of the two vectors you drew is zero. Now do it with vectors defined as ordered pairs of real numbers. What ordered pair is the zero vector? How is addition of ordered pairs defined? Can you find two ordered pairs that add up to the zero vector?

Not quite sure I understand what you're asking here. I'm going to look for my midterm and post the questions on here (only three questions). I think getting those questions down should be my top priority since they pretty much cover 1-2 months of this book.

Here's the midterm: http://hep.ucsb.edu/courses/ph20/mid.pdf
The solutions: http://hep.ucsb.edu/courses/ph20/mids.pdf

I'll look over the solutions for now.

Just looked over the solutions for cross products and dot products... really? It seems much more complicated when I read the problems, and the solutions are merely 2-4 lines? Come on...

Give me a dot product or cross product problem and I'll try to work it out.
 
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  • #10
Neoriginal said:
This is straight from the textbook:

"From the geometric point of view, a vector is a directed line segment. In order to describe a vector we must specify both its length and direction. If two vectors have the same length and and the same direction they are equal."
Yes, that's a way to describe vectors, but I doubt that your book defines them that way. It would really suck if it did. A vector (in a plane) is an ordered pair (x,y) of real numbers. Here, x and y are both real numbers, and (x,y) is usually not equal to (y,x). Addition of vectors is defined by

(a,b)+(c,d)=(a+c,b+d).

The product of a real number and a vector is defined by

a(c,d)=(ac,ad).

For ordered triples, or more generally, ordered n-tuples (x1,...,xn), where n is an arbitrary positive integer, the definitions are similar:

(x1,...,xn)+(y1,...,yn)=(x1+y1,...,xn+yn)

k(x1,...,xn)=(kx1,...,kxn)

You will mostly be concerned with the cases n=2 and n=3.

The zero vector [tex]\vec 0[/tex] is a vector with the property that [tex]\vec v+\vec 0=\vec 0+\vec v=\vec v[/tex] for all vectors [itex]\vec v[/itex]. Do you see any ordered pair with that property. Is there more than one? Can you find two ordered pairs [itex]\vec u=(u_1,u_2)[/itex] and [itex]\vec v=(v_1,v_2)[/itex] such that [tex]\vec u+\vec v=\vec 0[/tex]?

That's how you should solve the first problem in the first document you linked to.

Neoriginal said:
Connect the tail of vector A to the head of vector B. I somewhat know about Ax, Ay, Az, Bx, By, Bz, and how it doesn't matter in what way you connect these vectors.
This is because (a,b)+(c,d)=(c,d)+(a,b). Can you see how that's implied by the definition of the sum of two ordered pairs?

Neoriginal said:
Just looked over the solutions for cross products and dot products... really? It seems much more complicated when I read the problems, and the solutions are merely 2-4 lines? Come on...
It gets easier when you know the definitions. :wink:

Neoriginal said:
Give me a dot product or cross product problem and I'll try to work it out.
If [itex]\vec x[/itex] is parallel to [itex]\vec y[/itex], then what is [itex]\vec x\cdot(\vec y\times\vec z)[/itex]?
 
  • #11
I just looked at a cross product video on Youtube and am now trying to solve questions from my textbook.

Currently this one:

A = (2i - 3j + 7k)
B = (5i + j +2k)

From the math I've done, I have calculated AxB to be 35. Is that correct?

i = -13
j = 31
k = 17

I feel slightly more confident about the cross product now. I'll try learning the dot product next, then I'll be moving onto Newton's laws.
 
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  • #13
ehild said:
When having problems and you do not understand your textbook, browse the topic on the Net. You certainly find a place that fits to you. Try this for example : http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

ehild

Thank you for that website. Could you please tell me if my answer for the cross product of A and B are correct?
 
  • #14
Neoriginal said:
I just looked at a cross product video on Youtube and am now trying to solve questions from my textbook.

Currently this one:

|A| = (2i - 3j + 7k)
|B| = (5i + j +2k)

From the math I've done, I have calculated |A|x|B| to be 35. Is that correct?

i = -13
j = 31
k = 17

I feel slightly more confident about the cross product now. I'll try learning the dot product next, then I'll be moving onto Newton's laws.

Hint: I like to think of cross product as a vector product and a dot product as a scalar product because that way you can know what your answer should be :D

Considering you got a scalar value for your answer when calculating your cross (vector) product makes me think you got your terms mixed up somewhere. But I know where you got your value of 35 from, and it's not correct. You should leave the values you calculated in the i, j and k directions as just directions and put them in the form of a vector.
 
  • #15
NotEnuffChars said:
Hint: I like to think of cross product as a vector product and a dot product as a scalar product because that way you can know what your answer should be :D

Considering you got a scalar value for your answer when calculating your cross (vector) product makes me think you got your terms mixed up somewhere. But I know where you got your value of 35 from, and it's not correct. You should leave the values you calculated in the i, j and k directions as just directions and put them in the form of a vector.

Oh, I guess I did mix them up. So, are the values I got for i, j, and k incorrect? I've been looking at the dot product and it seems much easier than the cross product.

If I were to get the dot product of my original equation:

A = (2i - 3j + 7k)
B = (5i + j +2k)

A dot B = 10 + (-3) + 14

is that correct?

So far I have 1/3 of my midterm solved (http://hep.ucsb.edu/courses/ph20/mid.pdf)

I still need to learn problem 2 and problem 3. I have four days to learn this.
 
  • #16
Neoriginal said:
Thank you for that website. Could you please tell me if my answer for the cross product of A and B are correct?
No, the result of a cross product is a vector. http://en.wikipedia.org/wiki/Cross_product

AxB=-13 i + 31 j + 17 k.

So you got the components of the product vector, but you can not add them up as numbers. The cross product is the sum of three vectors, pointing in the directions of the unit vectors, i, j, k.

The dot product is a scalar. http://en.wikipedia.org /wiki/Dot_productYour result is OK for the dot product but you have to add up the three numbers.

ehild
 
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  • #17
ehild said:
No, the result of a cross product is a vector. http://en.wikipedia.org/wiki/Cross_product

AxB=-13 i + 31 j + 17 k.

So you got the components of the product vector, but you can not add them up as numbers. The cross product is the sum of three vectors, pointing in the directions of the unit vectors, i, j, k.

The dot product is a scalar. http://en.wikipedia.org /wiki/Dot_product


Your result is OK for the dot product but you have to add up the three numbers.

ehild

I'm confused here. What three numbers do I have to add up?
 
  • #18
Neoriginal said:
I'm confused here. What three numbers do I have to add up?

He was referring to the calculation of the scalar product.

Neoriginal said:
If I were to get the dot product of my original equation:

A = (2i - 3j + 7k)
B = (5i + j +2k)

A dot B = 10 + (-3) + 14

21
 
  • #19
Neoriginal said:
A = (2i - 3j + 7k)
B = (5i + j +2k)

From the math I've done, I have calculated AxB to be 35. Is that correct?
This shows that at the time you wrote this post, you still hadn't looked up the definition of the cross product. (A×B is a vector, not a number). How do you expect to be able to solve problems without knowing the definitions? You have to start by learning the definitions. Please post the definitions of "vector", "dot product" and "cross product" that you intend to use, and also your book's definitions of i,j and k.

Neoriginal said:
Oh, I guess I did mix them up. So, are the values I got for i, j, and k incorrect?
It would be incorrect if your i,j,k had been the wrong vectors, but when you put them equal to numbers your statements aren't even incorrect. :smile: (Again, you have to know the definitions).

Neoriginal said:
I've been looking at the dot product and it seems much easier than the cross product.
It is.

Neoriginal said:
If I were to get the dot product of my original equation:

A = (2i - 3j + 7k)
B = (5i + j +2k)

A dot B = 10 + (-3) + 14

is that correct?
Yes. A·B=10+(-3)+14=21. (The last equality is what ehild meant by "you have to add up the three numbers"). What do you get if A=2i-3k+7j, B=5i+j+2k instead? (Just checking if you understand the definitions).

By the way, you can copy and paste these symbols for the dot product and the cross product into your posts here: · ×
 
  • #20
Fredrik said:
Yes. A·B=10+(-3)+14=21. (The last equality is what ehild meant by "you have to add up the three numbers"). What do you get if A=2i-3k+7j, B=5i+j+2k instead? (Just checking if you understand the definitions).

By the way, you can copy and paste these symbols for the dot product and the cross product into your posts here: · ×

Would it be:

A × B = 17i - 19j - 33k

A · B = 10 + 7 + 6 = 23I've moved on to finding magnitudes.

Calculate the magnitude of A = (5, -4, 3)

[(5^2) + (-4^2) + (3^2)]^1/2 = (50)^1/2 Is that correct?

If I find the magnitude of |A × B| it would be:

A × B = 17i - 19j - 33k

[(17^2) + (-19^2) + (-33^2)]^1/2 = 41.7

I've also started looking into finding the angle between two vectors. I'll save that for my next post.
 
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  • #21
Neoriginal said:
Would it be:

A · B = 10 + 7 + 6 = 23

You made a small mistake, the third term is -6.

And write the square of a number '-a' as (-a)^2. (-4)^2=16, but (-4^2)=-16.


ehild
 
  • #22
Neoriginal said:
Would it be:

A × B = 17i - 19j - 33k

A · B = 10 + 7 + 6 = 23
As ehild said, you missed a minus sign in the dot product calculation. The cross product should have AkBi-AiBk=-8-4=-12 in front of the j, not -19. Your magnitude calculations are fine, except for the notational convention ehild mentioned.
 
  • #23
It turns out I've been studying the wrong things this whole weekend. What I really need to focus on is circular motion, momentum, work, and energy.
 
  • #24
For all of these, you need to understand vectors and vector products. The momentum is a vector, velocity and acceleration during circular motion are vectors, work is the dot product of the displacement (vector) and force (vector).

ehild
 

1. What is the dot product?

The dot product, also known as the scalar product, is a mathematical operation that takes two vectors as input and returns a single scalar value. It is calculated by multiplying the corresponding components of the two vectors and then summing them together.

2. How is the cross product different from the dot product?

The cross product, also known as the vector product, is a mathematical operation that takes two vectors as input and returns a vector that is perpendicular to both input vectors. Unlike the dot product, the cross product does not result in a scalar value but rather a vector.

3. What are Newton's three laws of motion?

Newton's laws of motion are a set of three fundamental principles that describe the behavior of objects in motion. The first law states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction.

4. How are Newton's laws used in physics?

Newton's laws are used to understand and predict the motion of objects in various situations. They serve as the foundation for many principles and equations in classical mechanics, such as the law of conservation of momentum and the equations of motion.

5. Can Newton's laws be applied to all objects?

Newton's laws can be applied to most objects and situations in everyday life. However, they are most accurate when dealing with objects that are not extremely small (such as atoms) or moving at very high speeds (such as particles near the speed of light).

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