Chapter 5 - Inner Product Spaces - 5.2 Orthogonal Sets of Vectors and Orthogonal Projections - Problems - Page 360: 6

$w=(\frac{2}{7}k, k)$ with k \in R$

We are given nonzero vectors $w=(w_1,w_2) \ne 0$ $v$ and $w$ are orthogonal if $(v,w)=0 \\ \rightarrow =0 \\ \rightarrow 7w_1-2w_2=0 \\ \rightarrow 7w_1=2w_2 \\ \rightarrow w_1=\frac{2}{7}w_2$ Hence, $w=(\frac{2}{7}k, k)$ with k \in R$