If vec{a} and vec{b} are two non-collinear ve | vedclass

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(B) Using the vector triple product formula $\vec{a} 	imes (\vec{b} 	imes \vec{c}) = (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{

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projection of $\vec{b}$ along a vector perpendicular to the vector $\vec{a}$

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(B) Using the vector triple product formula $\vec{a} 	imes (\vec{b} 	imes \vec{c}) = (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c}$, we have: $\vec{a} 	imes (\vec{b} 	imes \vec{a}) = (\vec{a} \cdot \vec{a}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{a}$ Dividing by $|\vec{a}|^2$: $\frac{\vec{a} 	imes (\vec{b} 	imes \vec{a})}{|\vec{a}|^2} = \frac{|\vec{a}|^2 \vec{b} - (\vec{a} \cdot \vec{b}) \vec{a}}{|\vec{a}|^2} = \vec{b} - \left( \frac{\vec{a} \cdot \vec{b}}{|\vec{a}|} ight) \frac{\vec{a}}{|\vec{a}|}$ Here, $\frac{\vec{a}}{|\vec{a}|}$ is the unit vector along $\vec{a}$, and $\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|}$ is the scalar projection of $\vec{b}$ onto $\vec{a}$. Thus, $\vec{b} - 	ext{proj}_{\vec{a}} \vec{b}$ represents the component of $\vec{b}$ perpendicular to $\vec{a}$.

If $\vec{a}$ and $\vec{b}$ are two non-collinear vectors, then $\frac{\vec{a} \times(\vec{b} \times \vec{a})}{|\vec{a}|^2}$ represents:

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