Answer
$\mathbf{v}\cdot \mathbf{w}=100$ and $\mathbf{v}\cdot \mathbf{v}=61$
Work Step by Step
The dot product, $\mathbf{v}\cdot \mathbf{w}$ as,
$\begin{align}
& \mathbf{v}\cdot \mathbf{w=}\left( -6\mathbf{i}-5\mathbf{j} \right)\cdot \left( -10\mathbf{i}-8\mathbf{j} \right) \\
& =\left( -6 \right)\mathbf{i}\cdot \left( -10 \right)\mathbf{i+}\left( -6 \right)\mathbf{i}\cdot \left( -8 \right)\mathbf{j+}\left( -5 \right)\mathbf{j}\cdot \left( -10 \right)\mathbf{i+}\left( -5 \right)\mathbf{j}\cdot \left( -8 \right)\mathbf{j} \\
& =60\left( \mathbf{i}\cdot \mathbf{i} \right)+48\left( \mathbf{i}\cdot \mathbf{j} \right)+50\left( \mathbf{j}\cdot \mathbf{i} \right)+40\left( \mathbf{j}\cdot \mathbf{j} \right) \\
& =60\left( 1 \right)+48\left( 0 \right)+50\left( 0 \right)+40\left( 1 \right)
\end{align}$
Solve ahead to get the result as,
$\begin{align}
& \mathbf{v}\cdot \mathbf{w}=60\left( 1 \right)+48\left( 0 \right)+50\left( 0 \right)+40\left( 1 \right) \\
& =60+0+0+40 \\
& =100
\end{align}$
The dot product, $\mathbf{v}\cdot \mathbf{v}$ as,
$\begin{align}
& \mathbf{v}\cdot \mathbf{v=}\left( -6\mathbf{i}-5\mathbf{j} \right)\cdot \left( -6\mathbf{i}-5\mathbf{j} \right) \\
& =\left( -6 \right)\mathbf{i}\cdot \left( -6 \right)\mathbf{i+}\left( -6 \right)\mathbf{i}\cdot \left( -5 \right)\mathbf{j+}\left( -5 \right)\mathbf{j}\cdot \left( -6 \right)\mathbf{i+}\left( -5 \right)\mathbf{j}\cdot \left( -5 \right)\mathbf{j} \\
& =36\left( \mathbf{i}\cdot \mathbf{i} \right)+30\left( \mathbf{i}\cdot \mathbf{j} \right)+30\left( \mathbf{j}\cdot \mathbf{i} \right)+25\left( \mathbf{j}\cdot \mathbf{j} \right) \\
& =36\left( 1 \right)+30\left( 0 \right)+30\left( 0 \right)+25\left( 1 \right)
\end{align}$
Solve ahead to get the result as,
$\begin{align}
& \mathbf{v}\cdot \mathbf{v}=36\left( 1 \right)+30\left( 0 \right)+30\left( 0 \right)+25\left( 1 \right) \\
& =36+0+0+25 \\
& =61
\end{align}$
