# 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.

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.

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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Gold Member
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?

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.

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.

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