# What is the dot product of <2,0,7> and <-4,9,-1 >?

The usual dot product for the vectors $x = \left({x}_{1} , {x}_{2} , \ldots , {x}_{n}\right)$ and $y = \left({y}_{1} , {y}_{2} , \ldots , {y}_{n}\right)$ in ${\mathbb{R}}^{n}$ is $x . y = {\sum}_{i = 1}^{n} {x}_{i} {y}_{i}$.
We apply it here : $\left(2 , 0 , 7\right) . \left(- 4 , 9 , - 1\right) = 2 \cdot \left(- 4\right) + 0 \cdot 9 + 7 \cdot \left(- 1\right) = - 15$