(a - b) middot c + b middot (c + a). a middot (a + 2c) + (2b - a) middot (a + 2c) - 2b middot (a + 2c). Taking a = 2i + j, b = 3i - j + 2k, c = 4i + 3k, calculate: the three dot products a middot b, a middot c, b middot c; the cosines of the angles between these vectors; the component of a (i) in the b direction, (ii) in the c direction; the projection of a (i) in the b direction, (ii) in the c direction. Repeat Exercise 11 with a = j + 3k, b = 2i - j + 2k, c = 3i - k. Find the unit vector with direction angles 1/3pi, 1/4pi, 2/3pi,