Question 14
- Given that
= 
and 
= 
, find the:
(i) angle between the vectors 
and
.
(ii) unit vector along
-
.
- P, Q, R and M are points in the 0XY plane. If
= 2i + 8j, 
= 11i – 12j and M divides 
internally in the ratio 3 : 7, find 
.
Observation
This question was reported to be unpopular among the candidates and majority of those who attempted it performed poorly. In part (a)(i), Candidates were expected to apply the formula cos θ = 
, where p and q are vectors and θ is the angle between p and q. Here, p = 
and q = 
+ 
= 
+ 
= 
. p•q = 
•
= 4 + 50 = 54. |p| = |
| = 
= 
. |q| = |
| = 
= 
. Therefore, the required angle was θ = cos-1(
= 32.95o. In part (b)(ii), if a =
-
=
- 
= 
.Then, |a| = |
-
| = 
= 7. Therefore, required unitvector â = 
= 
or i.