E, f, g, h And 2

x - 1. Consider the vectors u = and z = 3x - 2 -10x (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 R3 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 L 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]| = 2|lyll