Projection of vector a onto vector b using vector triple product [closed]

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We know the formula for projection of a on b $$ proj_{b} (a)=\left(\frac{a\cdot b}{||b||^2}\right)b = \left(\frac{a\cdot b}{b\cdot b}\right)b$$

and its length is called component of a in the direction of b written $$comp_b(a)=||proj_b(a)||=\frac{a\cdot b}{||b||}$$

How can we establish any relationship of above formulas with the following

Projection using vector triple product?

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1 Answer

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The sum of vector projection of a $\vec{a}$ onto a nonzero $\vec{b}$ and orthogonal projection of $\vec{a}$ onto the plane orthogonal to $\vec{b}$ is equal to $\vec{a}$.

More details are here $\rightarrow$ .

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