022 X :/Users/Garg%20Computer/Downloads/XPD127_Assignment_12_$1_2022.pdf Calculus does not cover vectors. 1. Show that r' + y? + 2? - 4x + by + 2 - - 0 is a sphere. Determine the centre and radius of the sphere. 2. Let a = 5i - 23 - 4k and b = 3i - k. Determine: (i) u = a + band || ull. (ii) the unit vector u in the direction of u. 3. Let a = 21 + 3j and b = i - 2j. Determine: (i) 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 + 2j - k and -2 + 3 + 2k 5. Suppose that | Ja - 2, 6 - 3 and the angle between a and & is 120 . Determine | 24 - 56 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 hp $7 fg f10 import sc