QUESTION 4
Suppose u; v and w are vectors in R3: Show by means of a counter example that
(i) (u × v) × w 6= u × (v × w) sometimes and that (5)
(ii) if u 6= 0; u × v = u × w then u need not be equal to w: (5)
[Hint: Use i = (1; 0; 0) ; j = (0; 1; 0) and k = (0; 0; 1)]
QUESTION 5
Let u = (-2; 0; 4) ; v = (3; -1; 6) and w = (2; -5; -5) : Compute
(i) the area of the parallelogram bounded by u and v (5)
(ii) the equation of the plane parallel to v and w passing through the tip of u. (5)
QUESTION 6
Let z1 = x + iy and z2 = a + ib with z1 = z2: Prove that
(i) x2 - a2 = (b - y) (b + y) and (5)
(ii) The arguments of z1 and z2 differ by a multiple of 2p (5)