Question

If `A = <3 ,3 ,-7 >`, `B = <5 ,8 ,-4 >` and `C=A-B`, what is the angle between A and C?

Answer 1

This is a special case of the dot-product; we know, without any further computation, that the angle `theta` between the two vectors is `pi/2`

Explanation:

Given:
`barA = <3,3,-7>`,
`barB = <5,8,-4>`,
`barC = barA - barB`

Subtract the components of `barB` from `barA`:

`barC = <(3 - 5), (3 - 8),(-7- -4)>`

`barC = <-2, -5,-3>`

Compute `barA*barC` by multiplying the respective components:

`barA*barC = (3)(-2) + (3)(-5) + (-7)(-3)`

`barA*barC = 0`

This is a special case of the dot-product; we know, without any further computation, that the angle `theta` between the two vectors is `pi/2`