In a parallelogram with position vectors of is and is with reference to as origin

MATHEMATICS · Single correct · A Level · Mathematics · Vectors · Vectors

Problem

In a parallelogram

OABC

with position vectors of

A

3\hat{i} + 4\hat{j}

and

C

4\hat{i} + 3\hat{j}

with reference to

O

as origin. A point

E

is taken on the side

BC

which divides it in the ratio of

2:1

. Also, the line segment

AE

intersects the line bisecting the

\angle AOC

internally at

P

CP

when extended meets

AB

at point

F

. The position vector of

P

is (1)

\hat{i} + \hat{j}

(2)

\frac{2}{3}(\hat{i} + \hat{j})

(3)

\frac{13}{3}(\hat{i} + \hat{j})

(4)

\frac{21}{5}(\hat{i} + \hat{j})