Candidates’ performance in this question was reported to be poor.  Majority of the candidates were not able to determine the unit vector in the direction of vector P.

The part(b) of the question was attempted by even fewer candidates.  The expected responses were as follows: /4i – 3j/ =   = 5.  Therefore, the required unit vector is given by 1/5(4i – 3j) = 4/5i – 3/5j.
(4i – 3j)·(8i + j) = 32 – 3 = 29.  /8i + j/ =  = .  Therefore if  x  is the required angle between the two vectors, cos x =  = 0.7194.  Thus from the tables,  x = 44.0°.