given the vectors u 3i - 2j k v i 2j

Question

Given the vectors u = 3i - 2j + k,   v = i + 2j - 4k,    w = -2i + 4j - 5k use vector methods to answer the following:

(a) Prove u, v and w can form the sides of a triangle;

(b)  Find the vector projection of u on v;

(c) Find the angle between u and v (to nearest degree);

(d)  Find a unit vector normal (perpendicular) to the plane of the triangle in (a).