1.8: Past-paper question 10

4PM1/1/June/2023 — Question 10 · 10 marks

O,A\displaystyle O, A and B\displaystyle B are fixed points such that
OA→=(b+1)i+bj\overrightarrow{OA} = (b + 1)\mathbf{i} + b\mathbf{j}
AB→=3i\overrightarrow{AB} = 3\mathbf{i}
The unit vector parallel to OB→\displaystyle \overrightarrow{OB} is 1734[(3a+2)i+bj]\displaystyle \frac{\sqrt{17}}{34} [(3a + 2)\mathbf{i} + b\mathbf{j}]
Given that a\displaystyle a and b\displaystyle b are constants where a>0\displaystyle a > 0 and b>0\displaystyle b > 0
find the exact value of
(i) a\displaystyle a
(ii) b\displaystyle b
(10)