1.14: Past-paper question 3

4PM1/2R/June/2024 — Question 3 · 6 marks

O,A\displaystyle O, A and B\displaystyle B are fixed points such that
∣OA→∣=35AB→=i+3ajOB→=7i+2aj\left| \overrightarrow{OA} \right| = 3\sqrt{5} \quad \overrightarrow{AB} = \mathbf{i} + 3a\mathbf{j} \quad \overrightarrow{OB} = 7\mathbf{i} + 2a\mathbf{j}
Given that a>0\displaystyle a > 0
(a) find the value of a\displaystyle a
(4)
(b) Hence find a unit vector parallel to OA→\displaystyle \overrightarrow{OA}
(2)