# 4.6.1 Vectors, Short Questions (Question 1 – 3)

Question 1:
Given that O (0, 0), A (3, 4) and B (9, 12), find in terms of the unit vectors,   $\underset{˜}{i}$ and   $\underset{˜.}{j}$
(a) $\stackrel{\to }{AB}$
(b) the unit vector in the direction of  $\stackrel{\to }{AB}$

Solution:
(a)

(b)

Question 2:
Given that A (3, 2), B (4, 6) and C (m, n), find the value of m and of n such that    $2\stackrel{\to }{AB}+\stackrel{\to }{BC}=\left(\begin{array}{c}12\\ -3\end{array}\right)$

Solution:

Question 3:
Diagram below shows a rectangle OABC and the point D lies on the straight line OB.

It is given that OD = 3DB.

Solution:

$\begin{array}{l}\stackrel{\to }{OB}=\stackrel{\to }{OA}+\stackrel{\to }{AB}=3\underset{˜}{x}+12\underset{˜}{y}\\ \\ \stackrel{\to }{OD}=3\stackrel{\to }{DB}\\ \frac{\stackrel{\to }{OD}}{\stackrel{\to }{DB}}=\frac{3}{1}\\ \stackrel{\to }{OD}:\stackrel{\to }{DB}=3:1\\ \therefore \stackrel{\to }{OD}=\frac{3}{4}\stackrel{\to }{OB}\\ \text{}=\frac{3}{4}\left(3\underset{˜}{x}+12\underset{˜}{y}\right)\\ \text{}=\frac{9}{4}\underset{˜}{x}+9\underset{˜}{y}\end{array}$