3.7: Unit vector, midpoint and parallel to an axis

0606/21/M/J/21 — Question 10 · 8 marks

Relative to an origin

O

,

\overrightarrow{OA} = \begin{pmatrix} 6 \\ -5 \end{pmatrix}

,

\overrightarrow{OB} = \begin{pmatrix} 10 \\ 3 \end{pmatrix}

,

\overrightarrow{OC} = \begin{pmatrix} x \\ y \end{pmatrix}

and

\overrightarrow{OD} = \begin{pmatrix} 12 \\ 7 \end{pmatrix}

.

(a)

Find the unit vector in the direction of

\overrightarrow{AB}

.

[3]

(b)

The point

A

is the mid-point of

BC

. Find the value of

x

and of

y

.

[2]

(c)

Point

E

lies on

OD

such that

OE:OD = 1:(1 + m)

. Find

m

such that

\overrightarrow{BE}

is parallel to the

x

-axis.

[3]