Question

How do you determine whether u and v are orthogonal, parallel or neither given `u=2i-2j` and `v=-i-j`?

Answer 1

u is not a scalar multiple of v. So, they are not parallel, The scalar product `u.v=0`. Therefore, they are orthogonal.

Explanation:

`u=<2, -2> and v = <-1, -1>`

The scalar product `u.v=`

`|u||v|cos`(angle between `u and v`)

`= (2)(-1) + ((-2)(-1) =-2 + 2 = 0`

So, cosine of the angle = 0. And so, the vectors are orthogonal.

If the vectors are parallel, they will be of the form <x, y> and k<x, y>,