1. find out the following integrals:
(b)∫sin2x cos32x dx
2. 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).