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(B) The orthogonal projection of a vector $\vec{a}$ on a non-zero vector $\vec{b}$ is defined as the component of $\vec{a}$ along the direction of $\v

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$\frac{(\vec{a} \cdot \vec{b}) \vec{b}}{|\vec{b}|^2}$

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(B) The orthogonal projection of a vector $\vec{a}$ on a non-zero vector $\vec{b}$ is defined as the component of $\vec{a}$ along the direction of $\vec{b}$.The formula for the projection of $\vec{a}$ on $\vec{b}$ is given by:$	ext{Proj}_{\vec{b}} \vec{a} = \left( \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} ight) \hat{b}$Since the unit vector $\hat{b} = \frac{\vec{b}}{|\vec{b}|}$,we substitute this into the formula:$	ext{Proj}_{\vec{b}} \vec{a} = \left( \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} ight) \left( \frac{\vec{b}}{|\vec{b}|} ight)$Simplifying the expression,we get:$	ext{Proj}_{\vec{b}} \vec{a} = \frac{(\vec{a} \cdot \vec{b}) \vec{b}}{|\vec{b}|^2}$

The orthogonal projection of vector $\vec{a}$ on vector $\vec{b}$ is:

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