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
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
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
Are the vectors \(\vec u = \left\langle {1,2, - 4} \right\rangle \), \(\vec v = \left\langle { - 5,3, - 7} \right\rangle \) and \(\vec w = \left\langle { - 1,4,2} \right\rangle \) in the same plane? Solution