# Vector Short Questions (Question 6 & 7)

Question 6:
The points P, Q and R are collinear. It is given that  $\stackrel{\to }{PQ}=4\underset{˜}{a}-2\underset{˜}{b}$  and  $\stackrel{\to }{QR}=3\underset{˜}{a}+\left(1+k\right)\underset{˜}{b}$ , where k is a constant. Find
(a)    the value of k,
(b)    the ratio of PQ : QR.

Solution:
(a)

(b)
$\begin{array}{l}\stackrel{\to }{PQ}=m\stackrel{\to }{QR}\\ \stackrel{\to }{PQ}=\frac{4}{3}\stackrel{\to }{QR}\\ \frac{\stackrel{\to }{PQ}}{\stackrel{\to }{QR}}=\frac{4}{3}\\ \therefore PQ:QR=4:3\end{array}$

Question 7:
Given that  $\underset{˜}{x}=3\underset{˜}{i}+m\underset{˜}{j}$ and  $\underset{˜}{y}=4\underset{˜}{i}-3\underset{˜}{j}$ , find the values of m if the vector  $\underset{˜}{x}$ is parallel to the vector $\underset{˜}{y}$ .

Solution: