Let U = (1,2,-2), V = (3, -1,3) and W = (5, 3, 4) be three...

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Let U = (1,2,-2), V = (3, –-1,–3) and W = (5, 3, 4) be three vectors of the 3-space with the same initial point. (a) Find the scalar triple product of U, V and W, that is, U. (V × W). (b) Find the vector and parametric equations of the plane that is parallel to both U and V and that passes through the origin. (c) Find the area of the parallelogram that has U and W as adjacent sides. Justify all your answers. Let U = (1,2,-2), V = (3, –-1,–3) and W = (5, 3, 4) be three vectors of the 3-space with the same initial point. (a) Find the scalar triple product of U, V and W, that is, U. (V × W). (b) Find the vector and parametric equations of the plane that is parallel to both U and V and that passes through the origin. (c) Find the area of the parallelogram that has U and W as adjacent sides. Justify all your answers.