Find ||2v-w|| if v=7i-5j and w=3i+2j

Question

May be a simple way to solve but I can't figure it out for the life of me, thanks in advance!

Answer 1

A simple way is to simplify the algebraic expression:

2v - w = 2(7i - 5j) - (3i + 2j) = 14i - 10j - 3i - 2j = 11i - 12j.

Because i and j are orthogonal vectors, then

||2v - w|| = √(11² + (-12)²) = √265