The orthogonal projection vector of $\vec{a}=2 \hat{i}+3 \hat{j}+3 \hat{k}$ on $\vec{b}=\hat{i}-2 \hat{j}+\hat{k}$ is

Question

Aicharya · Accepted Answer

Orthogonal projection vector $\vec{a}$ on $\vec{b}$ $\begin{aligned} & =\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2} \cdot \vec{b}=\frac{2-6+3}{1+4+1} 	imes(\hat{i}-2 \hat{j}+\hat{k}) \ & =\frac{-1}{6}(\hat{i}-2 \hat{j}+\hat{k})=\frac{1}{6}(-\hat{i}+2 \hat{j}-\hat{k})\end{aligned}$

The orthogonal projection vector of $\vec{a}=2 \hat{i}+3 \hat{j}+3 \hat{k}$ on $\vec{b}=\hat{i}-2…

Solution