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The projection of $=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ on $\hat{v}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{R}}$ is
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Verified Answer
The correct answer is:
$\frac{8}{\sqrt{14}}$
Projection of $a$ on $b=\frac{a \cdot b}{|b|}$
$$
\begin{aligned}
&=\frac{(3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}}) \cdot(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}})}{|2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}|} \\
&=\frac{6-3+5}{\sqrt{4+9+1}}=\frac{8}{\sqrt{14}}
\end{aligned}
$$
$$
\begin{aligned}
&=\frac{(3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}}) \cdot(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}})}{|2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}|} \\
&=\frac{6-3+5}{\sqrt{4+9+1}}=\frac{8}{\sqrt{14}}
\end{aligned}
$$
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