Homepage › Solution manuals › Gilbert Strang › Introduction to Linear Algebra › Exercise 1.2.9
If v2w2∕v1w1 = −1 then v2w2 = −v1w1 or v1w1 + v2w2 = v⋅w = 0 : perpendicular! The vectors (1,4) and (1,−1 4 ) are perpendicular.