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.