We substitute the vector components into the formula for the dot product:
Given:
[tex]\begin{gathered} u_{1\text{ = -2, }}u_{2\text{ = -3, }}\text{ }u_{3\text{ = -}}\text{ 1} \\ v_{1\text{ =}}-6,v_2=-4,v_3\text{ = 10} \end{gathered}[/tex][tex]\begin{gathered} u\ast v=u_1v_1\text{ }+\text{ }u_2v_{2\text{ }}+\text{ }u_3v_3\text{ } \\ We\text{ plug in what we know:} \\ u\ast v=u_1v_1\text{ }+\text{ }u_2v_{2\text{ }}+\text{ }u_3v_3\text{ } \\ =(-2)(-6)+(-3)(-4)+(_{}-1)(10) \\ \text{Calculate:} \\ u\ast v=\text{ 14} \end{gathered}[/tex]Therefore, the dot product is 14.
