Answer:
[tex]\begin{equation*} \langle-1316,-2303\operatorname{\rangle} \end{equation*}[/tex]
Explanation:
Given the vectors:
[tex]\begin{gathered} u=\langle4,-9\rangle \\ v=\langle-4,-7\rangle \end{gathered}[/tex]
The dot product of u and v is calculated below:
[tex]\begin{gathered} u\cdot v=4\times-4+-9\times-7 \\ =-16+63 \\ =47 \end{gathered}[/tex]
Therefore:
[tex]\begin{gathered} (u\cdot v)4v=47\times4\langle-4,-7\rangle \\ =329\langle-4,-7\rangle \\ =\langle-4\times329,-7\times329\rangle \\ =\langle-1316,-2303\operatorname{\rangle} \end{gathered}[/tex]
The indicated quantity is:
[tex]\begin{equation*} \langle-1316,-2303\operatorname{\rangle} \end{equation*}[/tex]
