Given the vectors:
[tex]\begin{gathered} u=\langle0,-2) \\ v=\langle-3,0\rangle \end{gathered}[/tex]
You need to apply Dot Product in order to find:
[tex]v\cdot v[/tex]
By definition, for:
[tex]\begin{gathered} A=\langle a_x,a_y\rangle \\ B=\langle b_x,b_y) \end{gathered}[/tex]
The Dot Product is:
[tex]A\cdot B=a_xb_x+a_yb_y[/tex]
In this case, you are multiplying the same vector by itself. Then, by definition:
[tex]v\cdot v=|v|^2[/tex]
Hence:
[tex]\begin{gathered} v\cdot v=(-3)(-3)+(0)(0) \\ v\cdot v=9 \end{gathered}[/tex]
Hence, the answer is:
[tex]v\cdot v=9[/tex]
