3.40: Section formula and vector equation for $m,n$

0606/12/O/N/21 — Question 7 · 8 marks

3.40 diagram

The diagram shows triangle

OAC

with

\overrightarrow{OA} = \mathbf{a}

,

\overrightarrow{OB} = \mathbf{b}

,

\overrightarrow{OC} = \mathbf{c}

. Point

B

lies on

AC

with

AB:BC = m:n

.

(a)(i)

Write down

\overrightarrow{AB}

in terms of

\mathbf{a}

and

\mathbf{b}

.

[1]

(a)(ii)

Write down

\overrightarrow{BC}

in terms of

\mathbf{b}

and

\mathbf{c}

.

[1]

(a)(iii)

Hence show that

\mathbf{b} = \dfrac{n\mathbf{a} + m\mathbf{c}}{m + n}

.

[2]

(b)

Given the printed vector equation in

m

and

n

, find

m

and

n

.

[4]