Recent Question

SEMESTER 1
ASSIGNMENT 02
Fixed closing date: 06 March 2017
Unique assignment number: 892294
QUESTION 1
If each component of a non-zero vector in R3 is doubled then the length of that vector is doubled.
Prove this statement. (5)
QUESTION 2
Suppose that u and v are two vectors such that jjujj = 2; jjvjj = 1 and u · v = 1. Find the angle
between u and v in radians. (5)
QUESTION 3
(a) Suppose the relationship Projau = Projav is true for some vectors a; u and w:
(i) Verify that u · v = v · a. (5)
(ii) Provide a counte example to show that u need not be equal to v in your example. (5)
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)

Disclaimer : LiveWebExperts.com provides assignment and homework help for guidance and reference purpose only. These papers are not to be submitted as it is. These papers are intended to be used for research and reference purposes only.