Verify Schwarz’s inequality for the 3-space vectors of Problem 11.6.

Data From Problem 11.6

For the following vectors in 3-space with x, y, z components as given, evaluate their magnitudes and the cosine of the angle between them (î, ĵ, and k̂ are the orthogonal unit vectors along the x, y, and z axes, respectively):

(a) A = î + 3ĵ + 2k̂; B = 5î + ĵ + 3k̂;

(b) A = 6î + 2j ̂+ 4 k̂; B = 2î + 2ĵ + 2k̂;

(c) A = 4î + 3ĵ + k̂; B = 3î + 4ĵ + 5k̂;

(d) A = 3î + 3ĵ + 2k̂;  B = - î -2ĵ + 3k̂.