answer all of the questions for me please :)

2. If a = 2i + k and b = -3j + 2k, find a unit vector u that is opposite in direction to v = 2a - b and a vector w having the same direction as v with a norm of 5. 3. Given vectors u, v E R2, and real scalar k, prove that k(u + v) = ku + kv. 4. Without actually finding the angle between each pair of vectors, determine if the angle is acute, right, or obtuse. (a) u = 3i - j, v = -2i + 2j (b) u = (-2, 5, 4), v = (3, 2, -1). 5. Find the exact value of the angle 0 between the vectors u = 3i - j and v = 2j + k. 6. Let Po, P1, and P2 be three non-collinear points in R3 that are vertices of a triangle whose area is 15. If a = PoPl and b = PoP2, find la x b|. 7. Let a = 2i - j + k and b = -i+ 2j - 2k. Find the area of the parallelogram determined by a and b. 8. Prove that u x v = -v x u. 9. Find the parametric equations of the line through the points (-2, 3, -1) and (1, -2, 4). Then find the points where this line intercepts the xy, yz, and xz planes. (continued on the next page)