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

## 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)

## 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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jbriggs444
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2019 Award
If we substruct (A-B) we get '0' because 1-1 = 0 Am I right Please check.
What is 1 - (-1) ?

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.

• Delta2
What is 1 - (-1) ?
1 - (-1) = 2

jbriggs444
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2019 Award
1 - (-1) = 2
Good. So if A = i + j + k and B = -i + -j + -k, what does that make A - B?

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

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)

## 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?

You cannot possibly get A -B = 0 unless A = B. Do you have A = B?
No, I don't A = B

jbriggs444
Homework Helper
2019 Award
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)?

If B = -i + -j + -k, what is (-B)?
-B = -(-i + -j + -k) = i + j + k
So what to do next?

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jbriggs444
Homework Helper
2019 Award
-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?

FactChecker
Gold Member
Just double-check your signs and account for double negatives correctly.

• Chestermiller
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?

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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'
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

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?

• Delta2
FactChecker
Gold Member
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.

• jbriggs444
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.

Ray Vickson
Homework Helper
Dearly Missed
'
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.

• jbriggs444
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.

haruspex
Homework Helper
Gold Member
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).

• David Lewis
'
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!