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 For vectors \(\mathbf{u}\) and \(\mathbf{v}\), we have \(\mathbf{p}=\operatorname{proj}_{\mathbf{v}}(\mathbf{u}).\) If \(\|\mathbf{u}\|=11\) and \(\|\mathbf{p}\|=6\), find \(\mathbf{p}\cdot\mathbf{u}.\)

 Feb 26, 2020
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vectors

\(\begin{array}{|rcll|} \hline p\cdot u &=& ||p|| * ||u|| * \cos(\alpha) \quad | \quad \cos(\alpha)= \dfrac{6}{11} \\\\ p\cdot u &=& 6 * 11 * \dfrac{6}{11} \\ \mathbf{p\cdot u} &=& \mathbf{36} \\ \hline \end{array}\)

 

laugh

 Feb 26, 2020

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