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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
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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 \(\dfrac{\|\mathbf{x}\|}{\|\mathbf{y}\|}\).

 

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

 

laugh

 Feb 28, 2020

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