Chapter 11.3, Problem 45ES

Show that if ${\text{v}}_1,{\text{v}}_2,\text{and}{\text{v}}_3$ are mutually orthogonal nonzero vectors in 3-space, and if a vector v in 3-space us expressed as $\text{v}={\text{c}}_{\text{1}}{\text{v}}_{\text{1}}+{\text{c}}_{\text{2}}{\text{v}}_{\text{2}}+{\text{c}}_{\text{3}}{\text{v}}_{\text{3}}$

Then the scalers are given by the formulas $c_i=\left(\text{v}\cdot {\text{v}}_i\right)/{‖{\text{v}}_i‖}^2,i=1,2,3$