3.39: Vector geometry in a quadrilateral

0606/12/M/J/21 — Question 3 · 5 marks

3.39 diagram

The diagram shows quadrilateral

OABC

with

\overrightarrow{OA} = \mathbf{a}

,

\overrightarrow{OB} = \mathbf{b}

,

\overrightarrow{OC} = \mathbf{c}

. Lines

OB

and

AC

meet at

P

with

AP:PC = 3:2

.

(a)

Find

\overrightarrow{OP}

in terms of

\mathbf{a}

and

\mathbf{c}

.

[3]

(b)

Given also that

OP:PB = 2:3

, show that

\mathbf{b} = \dfrac{2}{5}\mathbf{a} + \dfrac{3}{5}\mathbf{c}

.

[2]