1. Consider the vectors u = (a) Compute the area of the triangle inscribed by the vectors u and w. (b) Consider a plane that is parallel to the vectors v and w. Find two unit vectors perpendicular to this plane. (c) Let L be the line in R' that passes through the point (1, 2, 3) and is perpendicular to both of the vectors v and w. Find an equation for the line _ in vector form. (d) Find parametric equations for the line C. (e) Compute u . z in terms of x. (f) Find all values of x for which u and z are orthogonal. g) Compute the projection of the vector z onto u; your answer should be a vector whose components are expressions in terms of x. (h) Find a point P in R3 such that the points (0, 0, 0), (1, 1, 1), (1, -1, 0), and P form a rectangle. 2. Prove that for all vectors x, y E R", the vector x + 2y is orthogonal to the vector x - 2y if and only if | |x)| = 2llyll