We have the following vectors:
[tex]\begin{gathered} u=11i-5j=(11,-5), \\ v=-7i+10j=(-7,10)\text{.} \end{gathered}[/tex]
The dot product u • v is given by:
[tex]u\cdot v=(u_1,u_2)\cdot(v_1,v_2)=u_1\cdot v_1+u_2\cdot v_2\text{.}[/tex]
Replacing the coordinates above, we get:
[tex]u\cdot v=(11,-5)\cdot(-7,10)=11\cdot(-7)+(-5)\cdot10=-77-50=-127.[/tex]
Answer: -127
