8. (a) Let a = x2-2j -3k and b = -1-j+ yk. Determine the values of x and y given a is orthogonal to b and | | all = 91/bll [7 marks] (b) Suppose that | | all = 4, || b|| = 3 and the angle between a and b is 120. Deter- mine | | 3a - 5611. [6 marks] (c) Use vector methods to show that the triangle formed in 3-dimensional space with vertices A(3, 3, -3), B(4, 6, 3) and C(10, 4, 3) is right-angled. Determine the area of the triangle. [6 marks ] (d) The equation of a sphere is given by ( 20 - 20 0) 2 + ( y - yo ) ? + ( 2 - 20 ) 2 = 12 where r is the radius of the sphere and (x0, yo, Zo) is the centre of the sphere. Determine if the origin is inside the sphere given by x2 +y' + 22+ 8x - 6y+5% =12. [6 marks ]