MHT CET · Maths · Vector Algebra
The projection of \(\bar{a}=\hat{i}-2 \hat{j}+\hat{k}\) on \(\bar{b}=2 \hat{i}-\hat{j}+\hat{k}\) is
- A 5
- B \(5 \sqrt{6}\)
- C \(\frac{5}{\sqrt{6}}\)
- D \(\sqrt{6}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{\sqrt{6}}\)
Step-by-step Solution
Detailed explanation
Projection \(\bar{a}\) on \(\bar{b}\)
\(
=\frac{\bar{a} \cdot \bar{b}}{|\bar{b}|}=\frac{(\hat{i}-2 \hat{j}+\hat{k}) \cdot(2 \hat{i}-\hat{j}+\hat{k})}{\sqrt{(2)^2+(-1)^2+(1)^2}}=\frac{2+2+1}{\sqrt{6}}=\frac{5}{\sqrt{6}}
\)
\(
=\frac{\bar{a} \cdot \bar{b}}{|\bar{b}|}=\frac{(\hat{i}-2 \hat{j}+\hat{k}) \cdot(2 \hat{i}-\hat{j}+\hat{k})}{\sqrt{(2)^2+(-1)^2+(1)^2}}=\frac{2+2+1}{\sqrt{6}}=\frac{5}{\sqrt{6}}
\)
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