# If A = i + j + k and B = -I + -j + -k, then (A-B) will make angle with A?

#### Indranil

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)

#### studiot

Note you learn more from getting it wrong than getting it right.

If you did this in your opening post you would save lots of time and effort.

Hint. Think about what sort of object A, B and (A-B) are.

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#### topsquark

Forum Staff
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)
A hint: How do you find the angle between any two vectors?

-Dan

#### Indranil

A hint: How do you find the angle between any two vectors?

-Dan
By dot product of two vectors

#### Indranil

Note you learn more from getting it wrong than getting it right.

If you did this in your opening post you would save lots of time and effort.

Hint. Think about what sort of object A, B and (A-B) are.
Would it be unit vectors?

Forum Staff

#### Indranil

So, what is the vector A - B?

-Dan
A-B = A + (-B) = ( i + j + k) + (i + j+ k) = 2i + 2j + 2k

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#### HallsofIvy

Good. Notice that, since B= -A, A- B= A- (-A)= 2A. So what is the angle between A and 2A?

2 people

#### topsquark

Forum Staff
Good. Notice that, since B= -A, A- B= A- (-A)= 2A. So what is the angle between A and 2A?
Good spot. I hadn't noticed that.

-Dan

#### studiot

Good. Notice that, since B= -A, A- B= A- (-A)= 2A. So what is the angle between A and 2A?
Indranil
Note that 2 is a scalar. What happens to direction when you multiply (scalar * vector) ?

Note that you asked for diagrams.
I started to think about drawing htese like the last lot but you demonstrated some ability with algebra.

The foregoing discussion shows how much easier algebra is in this 3 dimensional case.

Do you still want diagrams ar can you now draw your own?

One thing you suggested when I asked what A, B and (A-B) are was that they are unit vectors.

Do you still think this or can you see why none of them are unit vectors?

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