Search any question & find its solution
Question:
Answered & Verified by Expert
If the position vectors of points $\mathrm{A}$ and $\mathrm{B}$ are $3 \hat{i}-2 \hat{j}+\hat{k}$
and $2 \hat{i}+4 \hat{j}-3 \hat{k}$ respectively, then what is the length of
$\overrightarrow{A B} ?$
Options:
and $2 \hat{i}+4 \hat{j}-3 \hat{k}$ respectively, then what is the length of
$\overrightarrow{A B} ?$
Solution:
1183 Upvotes
Verified Answer
The correct answer is:
$\sqrt{53}$
$\begin{aligned} \text { Given, } \overrightarrow{O A}=3 \hat{i}-2 \hat{j}+\hat{k} \\ & \overrightarrow{O B}=2 \hat{i}+4 \hat{j}-3 \hat{k} \\ & \overrightarrow{A B}=\overrightarrow{O B}-\overrightarrow{O A} \\ &=(2 \hat{i}+4 \hat{j}-3 \hat{k})-(3 \hat{i}-2 \hat{j}+\hat{k}) \\ &=\hat{i}(2-3)+\hat{j}(4+2)+\hat{k}(-3-1) \\ &=-\hat{i}+6 \hat{j}-4 \hat{k} \\ & \text { Length of } \mathrm{AB}=\sqrt{(-1)^{2}+(6)^{2}+(-4)^{2}} \\ &=\sqrt{1+36+16}=\sqrt{53} \end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.