This question was attempted by majority of the candidates and they performed very well
in it. Candidates' expected responses were:

In part (a), 6p - 5q = __6(5i +3j) - 5(4i + 7j) = 30i + 18j - 20i - 35j = 10i -17j __

/6p - 5q/ = √10²+ (-17)² = 19.723.

In part (b), mp + *nq *= 14i + *13j *=> m(5i + *3J) *+ *n(4i *+ *7J) *= 14i + *13j**. *Equating the like
terms we have: 5m + *4n *= 15 and 3m + *7n *= 13. Solving these two equations
simultaneously gave m = 2 and *n *= 1.

__
__In part (c), candidates were expected to recall that if 0 is the acute angle between p and
q, then Cosθ =

__p*g __ p*q = (5i + 3j)*(4i +7j) = 20 + 21 = 41.

/pl./q/

. /p/ =√5² + 3² =√34 , /q/ =√4² + 7² =√ 65.

Therefore, Cosθ =√41/√(34)√(65)= 0.872. This implied that θ = Cos-¹(0.872) = 29.29°. * *