1 Find in exact form the unit vector in the same direction as a = 4i – 7j. (3 marks)
2 In , and . P divides OA in the ratio 3 : 2 and Q divides
OB in the ratio 3 : 2
a Show that PQ is parallel to AB. (4 marks)
b Given that AB is 10 cm in length find the length of PQ. (1 mark)
Figure 1
3 Given that the resultant of the vectors a = 2pi – 5j and b = 6i – 3pj is parallel
to the vector c = 4i – 5j, find
a the value of p (4 marks)
b the resultant of the vectors a and b. (2 marks)
4 Given that point A has the position vector 4i + 7j and point B has the position
vector 10i + qj, where q is a constant, find
a the vector in terms of q (2 marks)
b Given further that , find the two possible values of q showing
detailed reasoning in your working. (5 marks)
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