Question

How will you write the vector joining points P(1, 3,2) and Q(4, 2, 1)? Also write the unit vector for $\underset{PQ}{\to }$

• A. $4\hat{i}+2\hat{J}+\hat{k},\frac{4\hat{i}+2\hat{j}+\hat{k}}{\sqrt{14}}$
• B. $3\hat{i}+\hat{J}+\hat{k},\frac{3\hat{i}+\hat{j}+\hat{k}}{\sqrt{11}}$
• C. $\hat{i}+3\hat{J}+2\hat{k},\frac{\hat{i}+3\hat{j}+2\hat{k}}{\sqrt{14}}$
• D. $3\hat{i}-\hat{J}-\hat{k},\frac{3\hat{i}-\hat{j}-\hat{k}}{\sqrt{11}}$

Answer 1

The correct option is D

$3\hat{i}-\hat{J}-\hat{k},\frac{3\hat{i}-\hat{j}-\hat{k}}{\sqrt{11}}$

For two point P and Q, the vector $\underset{PQ}{\to }$ looks like this

$\underset{PQ}{\to }$ = position vector $\overrightarrow{Q}$ – position vector $\overrightarrow{P}$

$=(4\hat{i}+2\hat{J}+\hat{k})-(\hat{i}+3\hat{j}+2\hat{k})\underset{PQ}{\to }=3\hat{i}-\hat{J}-\hat{k}$

And unit vector of $\underset{PQ}{\to }$ is written $\widehat{PQ}$ {a unit vector always wears a hat)

Which is given as $=\frac{\stackrel{⟶}{PQ}}{|PQ|}$

So $\widehat{PQ}=\frac{3\hat{i}-\hat{j}-\hat{k}}{\sqrt{3^2+1^2+1^2}}=\frac{3\hat{i}-\hat{j}-\hat{k}}{\sqrt{11}}$