Chapter 11.4, Problem 27ES

In each part, use a scalar triple product to determine whether the vectors lie in the same plane.

$\begin{array}{l}\left(\text{a}\right)\text{u}=〈\text{1,}-\text{2,}\text{1}〉\text{,}\text{v}=〈\text{3,}\text{0,}-\text{2}〉\text{,}\text{w}=〈\text{5,}-\text{4,}\text{0}〉\hfill \\ \left(\text{b}\right)\text{u}=\text{5i}-\text{2j}+\text{k,}\text{v}=\text{4i}-\text{j}+\text{k,}\text{w}=\text{i}-\text{j}\hfill \\ \left(\text{c}\right)\text{u}=〈\text{4,}-\text{8,}\text{1}〉\text{,}\text{v}=〈\text{2,}\text{1,}-\text{2}〉\text{,}\text{w}=〈\text{3,}-\text{4,}\text{12}〉\hfill \end{array}$