Determine if the vectors are orthogonal or not. u = 6i – 4j and v = 2i + 3j

Answer 1

Two vectors are orthogonal if their dot product is zero.

To find the Dot product 〈v₁,v₂〉•〈w₁,w₂〉= v₁w₁+v₂w₂

u = 6i - 4j = 〈6, -4〉

v = 2i + 3j = 〈2, 3〉

Dot product = (6)(2) + (-4)(3) = 12 - 12 = 0

So yes, the vectors are orthogonal.