# Question 7, Exercise 3.2

Solutions of Question 7 of Exercise 3.2 of Unit 03: Vectors. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

Find the components and the magnitude of $\overrightarrow{PQ}$, if $P(-1,2)$, $Q(2,-1)$.

As we have \begin{align}\overrightarrow{PQ}&=\overrightarrow{OQ}-\overrightarrow{OP}\\ &=(2\hat{i}-\hat{j})-(-\hat{i}+2\hat{j})\\ &=3\hat{i}-3\hat{j}\end{align} Also \begin{align}|\overrightarrow{PQ}|&=\sqrt{(3)^2+(3)^2}\\ &=\sqrt{18}=3\sqrt{2}.\end{align} Hence components of $\overrightarrow{PQ}$ are $3$, $-3$ and magnitude is $3\sqrt{2}$.

Find the components and the magnitude of $\overrightarrow{PQ}.$ If $P(-2,1),Q(2,3).$

Do yourself.

Find the components and the magnitude of $\overrightarrow{PQ}$. if $P(-1,1,2)$, $Q(2,-1,3)$.

As we have \begin{align}\overrightarrow{PQ}&=\overrightarrow{OQ}-\overrightarrow{OP}\\ &=(2\hat{i}-\hat{j}+3\hat{k})-(-\hat{i}+\hat{j}+2\hat{k})\\ &=3\hat{i}-2\hat{j}+\hat{k}\end{align} Also \begin{align}|\overrightarrow{PQ}|&=\sqrt{(3)^2+(-2)^2+(1)^2}\\ &=\sqrt{14}.\end{align} Hence components of $\overrightarrow{PQ}$ are $3$, $-2$, $1$ and magnitude is $\sqrt{14}$.

Find the components and the magnitude of $\overrightarrow{PQ}$. if $P(2,4,6)$, $Q(1,-2,3)$.

Do yourself.