Q57 / 150 · MHT CET 2021 (24 Sep Shift 1) · Mathematics
The projection of $\bar{a}=\hat{i}-2 \hat{j}+\hat{k}$ on $\bar{b}=2 \hat{i}-\hat{j}+\hat{k}$ is
- A5
- B$5 \sqrt{6}$
- Correct answerC$\frac{5}{\sqrt{6}}$
- D$\sqrt{6}$
Solution
Projection $\bar{a}$ on $\bar{b}$
$$
=\frac{\bar{a} \cdot \bar{b}}{|\bar{b}|}=\frac{(\hat{i}-2 \hat{j}+\hat{k}) \cdot(2 \hat{i}-\hat{j}+\hat{k})}{\sqrt{(2)^2+(-1)^2+(1)^2}}=\frac{2+2+1}{\sqrt{6}}=\frac{5}{\sqrt{6}}
$$
Hence, the correct answer is option: 'C'.