Chapter 13 - Vector Geometry - 13.4 The Cross Product - Exercises - Page 677: 34

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We calculate the cross product as follows: $\textbf{v}\times\textbf{w}=\begin{vmatrix}\textbf{i}&\textbf{j}&\textbf{k}\\3&-2&2\\4&-1&2\end{vmatrix}$ $=\textbf{i}(-4+2)-\textbf{j}(6-8)+\textbf{k}(-3+8)$ $=-2\textbf{i}+2\textbf{j}+5\textbf{k}$ $\textbf{u}\cdot(\textbf{v}\times\textbf{w})=$ $⟨1,1,0⟩\cdot⟨-2,2,5⟩=$ $(1\times-2)+(1\times2)+(0\times5)=0$