1.3: Find a vector parallel to AB

4PM1/2/June/2022 — Question 3 · 9 marks

O\displaystyle O, A\displaystyle A and B\displaystyle B are fixed points such that
OA→=pi−4jOB→=i+(2p+1)j\overrightarrow{OA} = p\mathbf{i}-4\mathbf{j} \qquad \overrightarrow{OB} = \mathbf{i}+(2p+1)\mathbf{j}
Given that
2 ∣OA→∣=∣OB→∣andp>0,\sqrt{2}\,\lvert\overrightarrow{OA}\rvert = \lvert\overrightarrow{OB}\rvert \quad \text{and} \quad p>0,
(a) find the value of p\displaystyle p.
(4)
Using this value of p\displaystyle p,
(b) find a unit vector that is parallel to AB→\displaystyle \overrightarrow{AB}.
(5)