Question 1211a

Vectors I: Basics, Dot and Cross Products

2011 Paper 1 Question 7i Variant

Question

Referred to the origin

{O, }

the points

{A}

and

{B}

are such that

{\overrightarrow{OA}=\mathbf{a}}

and

{\overrightarrow{OB}=\mathbf{b}.}

The point

{P}

on

{OA}

is such that

{OP:PA=1:2,}

and the point

{Q}

on

{OB}

is such that

{OQ:QB=4:1.}

The mid-point of

{PQ}

is

{M.}

Find

{\overrightarrow{OM}}

in terms of

{\mathbf{a}}

and

{\mathbf{b}}

and show that the area of triangle

{OMP}

can be written as

{k|\mathbf{a}\times \mathbf{b}|,}

where

{k}

is a constant to be found.

[6]

Answer

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