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