Chapter 11.3, Problem 46ES

Show that the three vectors ${\text{v}}_{\text{1}}=\text{3i}-\text{j}+\text{2k,}{\text{v}}_{\text{2}}=\text{i}+\text{j}-\text{k,}{\text{v}}_{\text{3}}=\text{i}-\text{5j}-\text{4k}$

are mutually orthogonal, and then use the result of Exercise 45 to find scalers $c_{\text{1}}\text{,}{c}_{\text{2}}\text{,}\text{and}{c}_{\text{3}}$ so that $c_{\text{1}}{\text{v}}_{\text{1}}+c_{\text{2}}{\text{v}}_{\text{2}}+c_{\text{3}}{\text{v}}_{\text{3}}=\text{i}-\text{j}+\text{k}$