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### Section 11.4 : Cross Product

1. If $$\vec w = \left\langle {1,0, - 3} \right\rangle$$ and $$\vec v = \left\langle {6, - 3, - 4} \right\rangle$$ compute $$\vec v \times \vec w$$.
2. If $$\vec w = \left\langle {1,0, - 3} \right\rangle$$ and $$\vec v = \left\langle {6, - 3, - 4} \right\rangle$$ compute $$\vec w \times \vec v$$.
3. If $$\vec a = 3\vec i - 2\vec j + 6\vec k$$ and $$\vec b = \left\langle {4, - 1, - 6} \right\rangle$$ compute $$\vec a \times \vec b$$.
4. Find a vector that is orthogonal to the plane containing the points $$P = \left( { - 4,2,6} \right)$$, $$Q = \left( { - 3,2,1} \right)$$ and $$R = \left( {2, - 1,1} \right)$$.
5. Find a vector that is orthogonal to the plane containing the points $$P = \left( { - 1,1,6} \right)$$, $$Q = \left( { - 2,3,2} \right)$$ and $$R = \left( { - 2,4,5} \right)$$.
6. Are the vectors $$\vec u = \left\langle { - 2,4, - 1} \right\rangle$$, $$\vec v = \left\langle {5, - 2, - 1} \right\rangle$$ and $$\vec w = \left\langle {3,4, - 3} \right\rangle$$ are in the same plane?
7. Are the vectors $$\vec u = \left\langle {1, - 1,4} \right\rangle$$, $$\vec v = \left\langle {4,2, - 2} \right\rangle$$ and $$\vec w = \left\langle { - 5,4, - 17} \right\rangle$$ are in the same plane?
8. Determine the value of b so that the vectors $$\vec u = \left\langle {4, - 5,3} \right\rangle$$, $$\vec v = \left\langle { - 2,0, - 5} \right\rangle$$ and $$\vec w = \left\langle {b, - 1,6} \right\rangle$$ are in the same plane.
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