If A = 2i + j – k, B = i + 2j + 3k, and C = 6i – 2j – 6k, then the angle between (A + B) and C will be

a. Calculate r = a - b + c, where a = 5i + 4j - 6k, b = -2i + 2j + 3k, and c = 4i + 3j + 2k. b. Calculate the angle between r and the z axis.

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5. Show that each of the given three vectors is a unit vector: 1/7(2i + 3j + 6k), 1/7(3i - 6j + 2k), 1/7(6i + 2j - 3k) Also, show that they are mutually perpendicular to each other.

Example 27 If i j k, 2i 5j, 3i 2j 3k and i 6j k are the position vectors of points A, B, C and D respectively, then find the angle between AB and CD . Deduce that AB and CD are collinear.