Browse Questions

# Find the projection of $\overrightarrow{i}+\overrightarrow{2j}-\overrightarrow{2k}$ on $\overrightarrow{2i}-\overrightarrow{j}+ \overrightarrow{5k}$

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• For any two vectors $\overrightarrow a \: and \overrightarrow b$, the projection of $\overrightarrow a \: on \: \overrightarrow b= \large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b|}$
$|\overrightarrow b|=\sqrt{4+1+25}=\sqrt{30}$
Projection of $\overrightarrow a \: on \: \overrightarrow b= \large\frac{\overrightarrow a.\overrightarrow b}{|\overrightarrow b|}=\large\frac{(1)(2)+(2)(-1)+(-2)(5)}{\sqrt{30}}$
$= \large\frac{2-2-10}{\sqrt{30}}=\large\frac{-10}{\sqrt{30}}$