Mathematics

Mathematics

Problem

In a parallelogram

OABC

with position vectors of

A

is

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

and

C

is

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 a.

\hat{i} + \hat{j}

b.

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

c.

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

d.

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

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