Given the vectors M = −10ax + 4ay − 8az and N = 8ax + 7ay − 2az, find:
(a) a unit vector in the direction of −M + 2N; (b) the magnitude of 5ax + N − 3M; (c) |M||2N|(M + N).
2. Vector A extends from the origin to (1, 2, 3), and vector B extends from the origin to (2, 3, −2). Find (a) the unit vector in the direction of (A − B); (b) the unit vector in the direction of the line extending from the origin to the midpoint of the line joining the ends of A and B.
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