7.8. Determine if points are collinear and calculate ratio of areas

G7. Vectors in two dimensions

Question

The diagram shows a parallelogram PQRS.
PR and QS intersects at T.
V is a point on SR such that 2 SV = VR.
SU : ST = 1 : 2.
\vec{SV}= a and \vec{SU}= b.

(a) Use vectors to determine if P, U and V lie on a straight line. [3]

(b) Find the ratio of

(i) \frac{the  area  of  \triangle{SUV}}{the area of \triangle{PUQ}} [1]
(ii) \frac{the  area  of  \triangle{SUV}}{the area of \triangle{PTQ}} [1]

Solution