(a). 

 Find x and y given that 

Given the three vectors a = 4i + 6j, b = 4i + 10j and c = 2i + 4j determine the magnitude of their resultant.

Given vectors a = 6i + 12j, b = 17i + 18j :

(i) Find the vector c = 2a – b and its magnitude correctly to 3 significant figures. (ii) Represent vector c in part (a)(i) on the x - y plane.

Given vectors (i) the vector a = 3i + 2 j , b = 8i +­ 3j and c = 2i + 4 j find:

(ii) a unit vector in the direction of d.

A boat sails due to North at speed of 120km/h and wind blows at speed of 40km/h due to east. Find actual speed of the boat. Use    

A boat crosses a river at a velocity of 30 km/h southwards. Water in the river flows at 5 km/h due East. By using the knowledge of vectors, calculate the resultant velocity of the boat. Give the answer correct to 2 decimal places.

If a = 2 i + 3 j, b = 19i – 15j and c = 5i – 7j, find the value of x such that xa + yc =b.

Find the direction cosines of C = 9i + 12j, hence show that the sum of the squares of these direction cosines is one.

Given that a = (3, 4), b = (1, ­4) and c = (5,2) determine:

(a) d = a + 4b – 2c ?

(b) magnitude of vector d , leaving your answer in the form m?n ?

(c) the direction cosines of d and hence show that the sum of the squares of these direction cosines is one.

Given the vectors x = 3i + 2j, y = 5i – 3j and z = 4i – 2j

(i) Find the resultant vector r = x + y + z and its direction.

(ii) Plot the three vectors on the same axes and hence indicate the magnitude of each vector [do not perform any calculation].

The position vectors of the points A, B and C are 4i - 3j , i +3j and -5i + j respectively. Find the vectors AB, BC and AC hence verify that AB + BC = AC (6 marks)

If  a = (4, 3), b=(-4, 1) and c=(2, 5), determine which of the vectors a + 2b and 3a + c is longer then the other.