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# help

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Let $$\mathbf{x}$$ and $$\mathbf{y}$$ be vectors such that $$\operatorname{proj}_{\mathbf{x}}(\mathbf{y})=\dbinom{5}{3}$$ and $$\operatorname{proj}_{\mathbf{y}}(\mathbf{x})=\dbinom{2}{-2}$$. Compute the ratio $$\dfrac{\|\mathbf{x}\|}{\|\mathbf{y}\|}$$.

Feb 28, 2020

#1
+24366
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Let $$x$$ and $$y$$ be vectors such that $$\operatorname{proj}_{\mathbf{x}}(\mathbf{y})=\dbinom{5}{3}$$and $$\operatorname{proj}_{\mathbf{x}}(\mathbf{y})=\dbinom{5}{3}$$.
Compute the ratio $$\dfrac{\|\mathbf{x}\|}{\|\mathbf{y}\|}$$.

$$\begin{array}{|rcll|} \hline \cos(\varphi) = \dfrac{\sqrt{8}}{\|\mathbf{x}\|} &=& \dfrac{\sqrt{34}}{\|\mathbf{y}\|} \\\\ \dfrac{\sqrt{8}}{\|\mathbf{x}\|} &=& \dfrac{\sqrt{34}}{\|\mathbf{y}\|} \\\\ \dfrac{\|\mathbf{x}\|}{\|\mathbf{y}\|} &=& \dfrac{\sqrt{8}}{\sqrt{34}} \\ \hline \end{array}$$

Feb 28, 2020