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# Find the projection of $\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{k}$ on $\overrightarrow{4i}-\overrightarrow{j}+\overrightarrow{2k}$

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• For any two vectors $\overrightarrow a \: and \overrightarrow b$, the projection of $\overrightarrow a \: on \: \overrightarrow b= \large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b|}$
$| \overrightarrow b|=\sqrt{16+1+4}=\sqrt{21}$
Projection of $\overrightarrow a\: on \overrightarrow b= \large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b|}=\large\frac{(3)(4)+(1)(-1)+(-1)(2)}{\sqrt{21}}$
$= \large\frac{12-1-2}{\sqrt{21}}= \large\frac{9}{\sqrt{21}}$
answered Jun 3, 2013