1. Let u be the vector parallel to the diagonal from the point (0, 0, 0) to the point (1, 1, 1). (0, 0, 1) (0, 1, 1) (a) (4 points) Express u in terms of i, j, and k. (1, 0, 1) (1, 1, 1) (0, 0, 0) (0, 1, 0) (b) (5 points) Find lul. (1, 0, 0) (1, 1, 0) (c) (6 points) Express the diagonal (line segment) from the point (0, 0, 0) to the point (1, 1, 1) as a parametric vector function r(t). (d) (4 points) Let w be the vector pararllel to the diagonal from the point (1, 1, 0) to the point (0, 0, 1). Express w in terms of i, j, and k. (e) (8 points) Find the angle between the vectors u and w. (f) (8 points) Find an equation of the plane that contains these two diagonals