3.3: Unit vector along OR and parallel condition

0606/22/F/M/22 — Question 10 · 8 marks

Relative to an origin OO, the position vector of point PP is 3i2j3\mathbf{i} - 2\mathbf{j} and the position vector of point QQ is 8i+13j8\mathbf{i} + 13\mathbf{j}.
(a)
The point RR is such that PQ=5PR\overrightarrow{PQ} = 5\overrightarrow{PR}. Find the unit vector in the direction OR\overrightarrow{OR}.
[5]
(b)
The position vector of SS relative to OO is mjm\mathbf{j}. Given that RS\overrightarrow{RS} is parallel to PQ\overrightarrow{PQ}, find the value of mm.
[3]