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### Section 5-4 : Cross Product

1. If $$\vec w = \left\langle {3, - 1,5} \right\rangle$$ and $$\vec v = \left\langle {0,4, - 2} \right\rangle$$ compute $$\vec v \times \vec w$$. Solution
2. If $$\vec w = \left\langle {1,6, - 8} \right\rangle$$ and $$\vec v = \left\langle {4, - 2, - 1} \right\rangle$$ compute $$\vec w \times \vec v$$. Solution
3. Find a vector that is orthogonal to the plane containing the points $$P = \left( {3,0,1} \right)$$, $$Q = \left( {4, - 2,1} \right)$$ and $$R = \left( {5,3, - 1} \right)$$. Solution
4. Are the vectors $$\vec u = \left\langle {1,2, - 4} \right\rangle$$, $$\vec v = \left\langle { - 5,3, - 7} \right\rangle$$ and $$\vec w = \left\langle { - 1,4,2} \right\rangle$$ are in the same plane? Solution