1.20: A, and are fixed points such that

4PM1/1R/June/2019 — Question 7 · 8 marks

\displaystyle O

,

\displaystyle A

,

\displaystyle B

and

\displaystyle C

are fixed points such that

\overrightarrow{OA}=8\mathbf{i}-6\mathbf{j}, \qquad \overrightarrow{OB}=15\mathbf{i}-6\mathbf{j}, \qquad \overrightarrow{OC}=8\mathbf{i}+\mathbf{j}.

(a) Find

\displaystyle \overrightarrow{BC}

as a simplified expression in terms of

\displaystyle \mathbf{i}

and

\displaystyle \mathbf{j}

.

(2)

(b) Find a unit vector parallel to

\displaystyle \overrightarrow{BC}

.

(2)

The point

\displaystyle M

is the midpoint of

\displaystyle OA

and the point

\displaystyle N

lies on

\displaystyle OB

such that

ON:NB=1:2.

(c) Show that the points

\displaystyle M

,

\displaystyle N

and

\displaystyle C

are collinear.

(4)