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1. Show that a2 +y' + 22 - 4x + 5y + 2 - = 0 is a sphere. Determine the centre and radius of t sphere. 2. Let a = 51 - 23 - 4k and b = 31 - k. Determine: (i) u = a + b and || ull. (ii) the unit vector u in the direction of u. 3. Let a = 21 + 3j and b = 1 - 23. Determine: () a . b. (ii) the length of a and b. (iii) the acute angle between a and b. 4. Determine the unit vectors which are orthogonal to both 32 + 23 - k and -2 + 3 + 2k. 5. Suppose that || a | | = 2, ||b | | = 3 and the angle between a and b is 120. Determine | | 2a - 5b||. 6. Use vector methods to decide whether the triangle with the vertices P(1, -3, -2), Q(2, 0, 4) and R(8, -2, 4) is right angled