# What is the dot product of <5,6,-3 > and <-4,8,-5 >?

$43$
The classic euclidian scalar product is given by the following formula : $\forall x = \left({x}_{1} , \ldots , {x}_{n}\right) , y = \left({y}_{1} , \ldots , {y}_{n}\right) \in {\mathbb{R}}^{n} : x . y = {\sum}_{i = 1}^{n} {x}_{i} {y}_{i}$.
We apply it here : $\left(5 , 6 , - 3\right) . \left(- 4 , 8 , - 5\right) = 5 \cdot \left(- 4\right) + 6 \cdot 8 + \left(- 5\right) \cdot \left(- 3\right) = - 20 + 48 + 15 = 43$