3.34: Parallel vectors and finding OP

0606/13/O/N/25 — Question 7 · 7 marks

The point

O

is the origin. Points

P

and

Q

are such that

\overrightarrow{PQ}

is in the same direction as

-\mathbf{i} + 5\mathbf{j}

.

(a)

Point

R

is such that

\overrightarrow{OR}

is in the same direction as

\overrightarrow{PQ}

and

|\overrightarrow{OR}| = 3\sqrt{26}

. Find

\overrightarrow{OR}

.

[3]

(b)

\overrightarrow{OP}

is in the same direction as

2\mathbf{i} - 3\mathbf{j}

and

\overrightarrow{OQ} = 10\mathbf{i} + 6\mathbf{j}

. Find

\overrightarrow{OP}

.

[4]