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If $\bar{a}=\hat{i}-2 \hat{j}+2 \hat{k}$ and $\bar{b}=2 \hat{i}-3 \hat{j}+\hat{k}$, then the component of $\bar{b}$ perpendicular to $\bar{a}$ is
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Verified Answer
The correct answer is:
$\frac{1}{3}(4 \hat{i}-5 \hat{j}+7 \hat{k})$
Given $\vec{a}=\hat{i}-2 \hat{j}-2 \hat{k} \quad$ and $\vec{b}=2 \hat{i}-3 \hat{j}+\hat{k} \quad$ now component of $\vec{b}$ perpendicular to $\vec{a}$ is given as
$\begin{aligned}
& =\vec{b}-\vec{b} \hat{a} \\
& =(2 \hat{i}-3 \hat{j}+\hat{k})-(2 \hat{i}-3 \hat{j}+\hat{k}) \frac{1}{3}(\hat{i}-2 \hat{j}-2 \hat{k}) \\
& =\frac{1}{3}(4 \hat{i}-5 \hat{j}-7 \hat{k})
\end{aligned}$
$\begin{aligned}
& =\vec{b}-\vec{b} \hat{a} \\
& =(2 \hat{i}-3 \hat{j}+\hat{k})-(2 \hat{i}-3 \hat{j}+\hat{k}) \frac{1}{3}(\hat{i}-2 \hat{j}-2 \hat{k}) \\
& =\frac{1}{3}(4 \hat{i}-5 \hat{j}-7 \hat{k})
\end{aligned}$
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