Search any question & find its solution
Question:
Answered & Verified by Expert
The projection of $\bar{a}=\hat{i}-2 \hat{j}+\hat{k}$ on $\bar{b}=2 \hat{i}-\hat{j}+\hat{k}$ is
Options:
Solution:
2531 Upvotes
Verified Answer
The correct answer is:
$\frac{5}{\sqrt{6}}$
Projection $\bar{a}$ on $\bar{b}$
$$
=\frac{\bar{a} \cdot \bar{b}}{|\bar{b}|}=\frac{(\hat{i}-2 \hat{j}+\hat{k}) \cdot(2 \hat{i}-\hat{j}+\hat{k})}{\sqrt{(2)^2+(-1)^2+(1)^2}}=\frac{2+2+1}{\sqrt{6}}=\frac{5}{\sqrt{6}}
$$
$$
=\frac{\bar{a} \cdot \bar{b}}{|\bar{b}|}=\frac{(\hat{i}-2 \hat{j}+\hat{k}) \cdot(2 \hat{i}-\hat{j}+\hat{k})}{\sqrt{(2)^2+(-1)^2+(1)^2}}=\frac{2+2+1}{\sqrt{6}}=\frac{5}{\sqrt{6}}
$$
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.