Finding unit vector normal to plane of the triangle

Question

Questions)

1. Calculate the following integrals:

(a)

(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).