Exercises : Vectors

Vectors

1.    If p and q are two vectors such that p = 3i + 5j + k and q = i + 2j -3k, determine the magnitude of p x q.                                                                                                    (4 marks)

Ans:

19.75

 2.    In the diagram, a and b are vectors such that cos A = 1/6. Given that a = i + j + pk and b = 2i + j + k, find the possible values.                                                                            (6 marks)

Ans:

 p = -26/5 or p = -2

  3.    Given that u = 3i + j - 2k, v = i – 4j + mk and w = 9i + 3j + (3n - 5)k are three vectors, where m and n are scalars.

a)    If u and v are perpendicular, calculate the value of m.                               (2 marks)

    b)    If u and w are parallel, calculate the value of n.                                       (3 marks)

Ans:

a)    m = -1/2

b)    n = -1/3

4.    The position vectors of points A and B are i – 2j + 4k and 3i + j – 2k respectively. Find

a)    The magnitude of AB                                                                                 (3 marks)

b)    The position vector of a point R which divides the line AB in the ratio 3 : 5                                                                                                                         (3 marks)

Ans:

a)    7

b)    7/4 i – 7/8 j + 7/4 k

 5.    Three vectors a , b and c are such that a x b = i + 2k and b x c = i – 4j – k, where i , j and k are unit vectors. Express (a – 3c) x (a + 2b – 3c) in terms of i , j and k.                                                                                                                             

  (6 marks)

Ans:

8i – 24j – 2k