The projection of $\bar{a}=\hat{i}-2 \hat{j}+\hat{k}$ on $\bar{b}=2 \hat{i}-\hat{j}+\hat{k}$ is

The projection of $\bar{a}=\hat{i}-2 \hat{j}+\hat{k}$ on $\bar{b}=2 \hat{i}-\hat{j}+\hat{k}$ is
  1. 5
  2. $5 \sqrt{6}$
  3. $\frac{5}{\sqrt{6}}$
  4. $\sqrt{6}$

Solution

Projection $\bar{a}$ on $\bar{b}$ $=\frac{\bar{a} \cdot \bar{b}}{|\bar{b}|}=\frac{(\hat{i}-2 \hat{j}+\hat{k}) \cdot(2 \hat{i}-\hat{j}+\hat{k})}{\sqrt{(2)^2+(-1)^2+(1)^2}}=\frac{2+2+1}{\sqrt{6}}=\frac{5}{\sqrt{6}}$

Asked in: MHT CET 2021 (24 Sep Shift 1)

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