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### Section 11.4 : Cross Product

1. If $$\vec w = \left\langle {3, - 1,5} \right\rangle$$ and $$\vec v = \left\langle {0,4, - 2} \right\rangle$$ compute $$\vec v \times \vec w$$.

Show Solution

Not really a whole lot to do here. We just need to run through one of the various methods for computing the cross product. We’ll be using the “trick” we used in the notes.

\begin{align*}\vec v \times \vec w & = \left| {\begin{array}{*{20}{c}}{\vec i}&{\vec j}&{\vec k}\\0&4&{ - 2}\\3&{ - 1}&5\end{array}} \right|\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{\vec i}&{\vec j}\\0&4\\3&{ - 1}\end{array}\\ & = 20\vec i - 6\vec j + 0\vec k - 0\vec j - 2\vec i - 12\vec k = \require{bbox} \bbox[2pt,border:1px solid black]{{18\vec i - 6\vec j - 12\vec k}}\end{align*}