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Algebraic Vectors (15 Marks) 5. Given the vectors, u = 31 - 4) - 5k , # = (2, 3, -1) and w = (-5,2, -3), find ... a) 25 - 3w b) |wl (1) (1) c) a unit vector in the same direction d) the angle between u and w (to 1 as u. decimal place) (1) (2) a vector that is parallel to w but f) A vector that is perpendicular to points in the opposite direction both i and w. and has a different magnitude. (2) (2) 6. Given N(6,2) and MN = (-3,4), find OM. (2) 7. Calculate the exact value of (3a - 2b) - (2a + b) if jal # 4. |b| # 6. and the angle between a and b is 150 (3) 8. If a = (5, -2,3) and d = (n, Sk, 6n), determine a value for n and k that will make and d perpendicular. (2)