1. If P(x, y, z) is any point on the surface of a sphere centered at (2, 3, 4), obtain the equation of the sphere using vectors.

2. Given A = a x cos α + a y sin α, B = a x cos β - a y sin β, and C =a x cos β + a y sin β, show that each is a unit vector. If β α, sketch these vectors and show that they are coplanar. Using these vectors ob- tain the following trigonometric identities: sin(α + β) = sin α cos β + cos α sin β, and sin(α - β) = sin α cos β - cos α sin β.