determine all vectors in R2 that are orthogonal to u 4 2Sol

determine all vectors in R^2 that are orthogonal to u = (4, 2).

Solution

Let the vector orthogonal to u be v.

v = (v₁,v₂)

u.v = 0 (since, dot product of orthogonal vector is zero)

4v₁ + 2v₂ = 0

2v₁ = -v₂

Therefore, all vectors which are orthogonal to u is (k,-2k) where k belongs to R.