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

1 Answer
Aug 6, 2016

Answer:

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>,