If A = i + j + k and B = -I + -j + -k, what will be an angle...

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Homework Statement


If A = i + j + k and B = -i + -j + -k , then (A-B) will make angle with A? What is the concept behind it, could you please explain with a diagram? (this is the part from scalar and vector)

Homework Equations




The Attempt at a Solution


If we substruct (A-B) we get '0' because 1-1 = 0 Am I right Please check.
 

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  • #2
jbriggs444
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If we substruct (A-B) we get '0' because 1-1 = 0 Am I right Please check.
What is 1 - (-1) ?
 
  • #3
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When you figure out where you made a mistake by answering the question jbriggs posted, use the dot product between (A-B) and A to figure out the angle.
##\vec{(A-B)}\vec{A}=|(A-B)||A|\cos\phi##, where ##\phi## is the angle.
 
  • #5
jbriggs444
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1 - (-1) = 2
Good. So if A = i + j + k and B = -i + -j + -k, what does that make A - B?
 
  • #6
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When you figure out where you made a mistake by answering the question jbriggs posted, use the dot product between (A-B) and A to figure out the angle.
##\vec{(A-B)}\vec{A}=|(A-B)||A|\cos\phi##, where ##\phi## is the angle.
Good. So if A = i + j + k and B = -i + -j + -k, what does that make A - B?
If we add A + (-B) = A-B so A + (-B) = i + j + k + (-i + -j + -k) = i + j+ k+ -i +-j + -k = 0
 
  • #7
Ray Vickson
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Homework Statement


If A = i + j + k and B = -i + -j + -k , then (A-B) will make angle with A? What is the concept behind it, could you please explain with a diagram? (this is the part from scalar and vector)

Homework Equations




The Attempt at a Solution


If we substruct (A-B) we get '0' because 1-1 = 0 Am I right Please check.
You cannot possibly get A -B = 0 unless A = B. Do you have A = B?
 
  • #9
jbriggs444
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If we add A + (-B) = A-B so A + (-B) = i + j + k + (-i + -j + -k) = i + j+ k+ -i +-j + -k = 0
If B = -i + -j + -k, what is (-B)?
 
  • #10
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If B = -i + -j + -k, what is (-B)?
-B = -(-i + -j + -k) = i + j + k
So what to do next?
 
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  • #11
jbriggs444
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-B = -(-i + -j + -k) = i + j + k
So what to do next?
So work that last bit again. A - B = A + -B. What is A - B?
 
  • #12
FactChecker
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Just double-check your signs and account for double negatives correctly.
 
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  • #13
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So work that last bit again. A - B = A + -B. What is A - B?
A + -B = i + j + k + i + j + k = 2i + 2j + 2k
what to do next?
 
  • #14
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You asked for a geometrical representation; do you understand how to graph a vector? A
Vector is different from a scalar because unlike a scalar, vectors have both a magnitude (length) and a direction (angle). Graphing the point A(1,2) is simple enough, A lies a distance 1 in the positive x direction and 2 in the positive y direction. With the VECTOR <1,2> the values 1, and 2 act as weights on standard unit vectors i = <1,0> and j = <0,1> so A would be the vector sum of 1*<1,0> + 2*<0,1> if you can begin by drawing these two vectors in the x-y plane then you will have a better understanding of what the geometrical representation of a vector is
 
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  • #15
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'
You asked for a geometrical representation; do you understand how to graph a vector? A
Vector is different from a scalar because unlike a scalar, vectors have both a magnitude (length) and a direction (angle). Graphing the point A(1,2) is simple enough, A lies a distance 1 in the positive x direction and 2 in the positive y direction. With the VECTOR <1,2> the values 1, and 2 act as weights on standard unit vectors i = <1,0> and j = <0,1> so A would be the vector sum of 1*<1,0> + 2*<0,1> if you can begin by drawing these two vectors in the x-y plane then you will have a better understanding of what the geometrical representation of a vector is
I know how to draw but this is not my question my question is 'If A = i + j + k and B = -i + -j + -k , then (A-B) will make an angle with A?' I have done so far above as directed
 
  • #16
haruspex
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then (A-B) will make an angle with A?'
Do you know how to find the angle between two vectors? What do you know about dot products?
 
  • #17
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A + -B = i + j + k + i + j + k = 2i + 2j + 2k
what to do next?
Can you express that answer in terms of A? That should tell you something about the angle between it and A without needing a diagram.
 
  • #18
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When you figure out where you made a mistake by answering the question jbriggs posted, use the dot product between (A-B) and A to figure out the angle.
##\vec{(A-B)}\vec{A}=|(A-B)||A|\cos\phi##, where ##\phi## is the angle.

'
I know how to draw but this is not my question my question is 'If A = i + j + k and B = -i + -j + -k , then (A-B) will make an angle with A?' I have done so far above as directed

If you know how to draw these vectors than i don't see how you can't find the angle.
Also, I already answered your question about the angle in the second post. All you have to do is plug in the numbers.
 
  • #19
Ray Vickson
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I know how to draw but this is not my question my question is 'If A = i + j + k and B = -i + -j + -k , then (A-B) will make an angle with A?' I have done so far above as directed

You say you know how to draw the vectors A and (A-B). Have you actually done the drawings? If you had done that (correctly) the answer would be obvious.
 
  • #20
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If we substruct (A-B) we get '0' because 1-1 = 0
You need to use vector addition, not arithmetic addition. You need to find the directions of vectors A and B in order to solve the problem. The magnitudes are irrelevant.
 
  • #21
haruspex
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You need to use vector addition, not arithmetic addition. You need to find the directions of vectors A and B in order to solve the problem. The magnitudes are irrelevant.
Indranil did use vector addition. The error was confusing 1-1 with 1-(-1).
 
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  • #22
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'
I know how to draw but this is not my question my question is 'If A = i + j + k and B = -i + -j + -k , then (A-B) will make an angle with A?' I have done so far above as directed
which is precisely why I asked you to diagram these vectors, presumably you understand basic right angle trigonometry and have been introduced to the notion of a dot product and its relation to the magnitudes of vectors and the angle between them, my post was only meant to help guide you in that direction. Unfortunately nobody here is going to continue to spoon feed you answers, you've got to think about it a bit more here. If you are so lost to the point where you can't even understand why you're lost then you should take a walk and think about that. Return when you at least understand where you're getting confused and we can help guide you a bit more. Good luck!
 

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