2. {8 points} Consider the vectors $$v_1 = \begin{bmatrix} 1 \\ a \\ 2 \end{bmatrix} \text{ and } v_2 = \begin{bmatrix} b \\ -1 \\ 1 \end{bmatrix}$$ where a and b are parameters. What should be the condition on a and b for the projection of $v_1$ on $v_2$ to have the same magnitude as the projection of $v_2$ on $v_1$?
Added by Amparo N.
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e., $$ \|\text{proj}_{v_2} v_1\| = \|\text{proj}_{v_1} v_2\| $$ $$ \left\| \frac{v_1 \cdot v_2}{\|v_2\|^2} v_2 \right\| = \left\| \frac{v_2 \cdot v_1}{\|v_1\|^2} v_1 \right\| $$ $$ \frac{|v_1 \cdot v_2|}{\|v_2\|^2} \|v_2\| = \frac{|v_2 \cdot v_1|}{\|v_1\|^2} Show more…
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