Explanation:
Here we have to compute the dot product:
[tex]v\cdot w[/tex]
We know that:
[tex]v = <6, 7, -3> \\ \\ w = <-7, 5, 2>[/tex]
So for any two vectors:
[tex]A = <x_{1}, y_{1}, z_{1}> \\ \\ B = <x_{2}, y_{2}, z_{2}>[/tex]
The dot product:
[tex]A\cdot B=x_{1}y_{1}+x_{2}y_{2}+z_{1}z_{2}[/tex]
Therefore:
[tex]v\cdot w=(6)(-7)+(7)(5)+(-3)(2) \\ \\ \boxed{v\cdot w=-13}[/tex]
