1.10: Past-paper question 4

4PM1/2R/June/2023 — Question 4 · 6 marks

\displaystyle O, A

and

\displaystyle B

are fixed points such that

\overrightarrow{OA} = 5\mathbf{i} + 7\mathbf{j} \quad \overrightarrow{AB} = a\mathbf{i} + 16\mathbf{j} \quad \mathrm{and} \quad |\overrightarrow{OB}| = 5\sqrt{29}

(a) Find the possible values of

\displaystyle a

(4)

Given that

\displaystyle a > 0

(b) find a unit vector that is parallel to

\displaystyle \overrightarrow{AB}

(2)