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

Aug 6, 2016

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

#### Explanation:

$u = < 2 , - 2 > \mathmr{and} v = < - 1 , - 1 >$

The scalar product $u . v =$

$| u | | v | \cos$(angle between $u \mathmr{and} v$)

= (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>,