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Assignment Problems Notice
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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 11.4 : Cross Product
- If \(\vec w = \left\langle {1,0, - 3} \right\rangle \) and \(\vec v = \left\langle {6, - 3, - 4} \right\rangle \) compute \(\vec v \times \vec w\).
- If \(\vec w = \left\langle {1,0, - 3} \right\rangle \) and \(\vec v = \left\langle {6, - 3, - 4} \right\rangle \) compute \(\vec w \times \vec v\).
- If \(\vec a = 3\vec i - 2\vec j + 6\vec k\) and \(\vec b = \left\langle {4, - 1, - 6} \right\rangle \) compute \(\vec a \times \vec b\).
- 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 \(R = \left( {2, - 1,1} \right)\).
- 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 \(R = \left( { - 2,4,5} \right)\).
- 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?
- 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?
- 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.