Resnick Halliday Krane Unit Vectors question

In summary: If the answer is in the 4th quadrant, add 360 degrees to the answer the calculator gives you. This will always give you the correct angle in the 1st quadrant.
  • #1
Neek 007
41
0
The start of a new school year in Ap physics C, and our favorite engineering professors causing students distress! Maybe the champions of the textbook can help me out... = )

Homework Statement



1. Two vectors are given by
a = 4i hat - 3j hat + k hat
b = -i hat +j hat + 4k hat.

Find
a) a + b
b) a-b
C) vector c such that a -b +c = 0

2.Given two vectors
a = 4i hat - 3j hat
b = 6i hat + 8j hat

Find the magnitudes and directions (with the +x axis) of

a)a
b)b
c)a+b
d)b-a
e)a-b

Homework Equations


components equations
etc

The Attempt at a Solution

on question 1, I've gotten parts a and b, but running into difficulty proving a-b + c=0.
i took a-b from part b and replaced it into the equation.

C)
a - b = 3i hat + 2j hat

3i hat + 2j hat + c = 0

3i hat + 2j hat + (azk hat + bz k hat)

3i hat + 2j hat + (1 + 4)k hat

3i hat + 2j hat + 5k hat = 0

i solved for vector c as 5k hat, but i am not sure if this satisfies the solution, as k hat runs into the z direction.
on question 2,

e) a - b

a = 4i hat -3j hat
b= 6i hat +8j hat

a-b=-2i hat - 11j hat

-2i hat = cx = -2
-11j hat = cy = -11

[itex]\sqrt{125}[/itex] = 11.180

tan [itex]\Phi[/itex] = (-11/-2) = 79.650 degrees

vector c = 11.180 at 79.650 degrees with +x-axis.

this is the answer i had gotten, but the book answer decides to choose 260 degrees. i have looked at my positive and negative symbols for my angle measure, but cannot meet the same number.

Any help is much appreciated :)
 
Physics news on Phys.org
  • #2
Neek 007 said:
on question 1, I've gotten parts a and b, but running into difficulty proving a-b + c=0.
i took a-b from part b and replaced it into the equation.

C)
a - b = 3i hat + 2j hat
Redo that subtraction.

on question 2,

e) a - b

a = 4i hat -3j hat
b= 6i hat +8j hat

a-b=-2i hat - 11j hat

-2i hat = cx = -2
-11j hat = cy = -11

[itex]\sqrt{125}[/itex] = 11.180

tan [itex]\Phi[/itex] = (-11/-2) = 79.650 degrees

vector c = 11.180 at 79.650 degrees with +x-axis.
Hint: What quadrant should your answer be in?
 
  • #3
For Question 1 C consider it to be a normal algebraic equation. If it were asking you for a number, z, such that if x = 3, y = 5, x - y + z = 0 What would you do? You seem to be thinking that the vector c has to be the z component of this new a-b vector, but it isn't! It is its own unique vector [itex] \vec{c} = c_{x}\hat{i} + c_{y}\hat{j} + c_{z}\hat{k} [/itex]
 
  • #4
Keep in mind that to add two vectors that are expressed in component form, you add them component-wise. In other words, the x-component of the resultant is the sum of the x-components of all the individual vectors, and likewise for y and z. Bearing that in mind, I think the best approach for part C is to use a vector c = (cx, cy, cz) whose components are unknown (note: boldface denotes vectors). This way you have three unknowns, but you also have three equations (which come from the component-wise summation) so you can solve for them all.
 
  • #5
Great! I got both of them. for question 1 it looks like i just got a bit lazy. question 2 i did indeed needed to refer to the quadrant. For my future reference, i should always check which quadrant i am going to end up in at the end.

oh yea another small question. What does "with + x axis" mean? does it mean with respect to the x axis?

Thanks alot!
 
  • #6
Neek 007 said:
oh yea another small question. What does "with + x axis" mean? does it mean with respect to the x axis?
Yes. (As opposed to the negative x axis.)
 
  • #7
Neek 007 said:
For my future reference, i should always check which quadrant i am going to end up in at the end.

A handy rule to remember is: When taking an inverse tangent on a calculator, if the answer is in the 2nd or 3rd quadrant, add 180 degrees to the answer that the calculator gives you.
 

1. What is the Resnick Halliday Krane Unit Vectors question?

The Resnick Halliday Krane Unit Vectors question is a physics problem that involves finding the unit vectors of a given vector. It is commonly used in introductory physics courses to help students understand the concept of unit vectors and their applications in solving problems.

2. Why is it important to understand unit vectors?

Unit vectors are essential in physics because they represent the direction of a vector without any consideration of its magnitude. They are used in many physical equations and calculations, making it crucial for students to understand their properties and how to manipulate them in problem-solving.

3. How do you approach solving the Resnick Halliday Krane Unit Vectors question?

The first step is to understand the given vector and its components. Then, use the definition of unit vectors to find the unit vector in each direction (x, y, and z). Finally, combine the unit vectors to form the complete unit vector in three-dimensional space.

4. Are there any tips for solving the Resnick Halliday Krane Unit Vectors question?

One tip is to draw a diagram to visualize the given vector and its components. This can help in understanding the problem and identifying the unit vectors needed. Additionally, always double-check your calculations and make sure the final unit vector has a magnitude of one and points in the correct direction.

5. How can I improve my understanding of unit vectors and their applications?

Practice is key in mastering the concept of unit vectors. Try solving different problems that involve unit vectors to become familiar with their properties and how to manipulate them. Additionally, seeking help from a teacher or tutor can also improve your understanding and clarify any doubts you may have.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Precalculus Mathematics Homework Help
Replies
18
Views
419
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
16K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
30K
  • Calculus and Beyond Homework Help
Replies
5
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
844
Back
Top