What is the dot product of <-8,5,2 >  and <-3,1,7 > ?

Jan 10, 2016

$43$

Explanation:

For any 2 vectors $A = \left({a}_{1} , {a}_{2} , \ldots , {a}_{n}\right) \mathmr{and} B = \left({b}_{1} , {b}_{2} , \ldots , {b}_{n}\right)$ in a finite dimensional real or complex vector space X, the Euclidean inner product (dot product) is a real or complex number given by
$A \cdot B = {a}_{1} {b}_{1} + {a}_{2} {b}_{2} + \ldots + {a}_{n} {b}_{n}$.

So in this particular case, we work in $X = {\mathbb{R}}^{3}$ and get

$\left(- 8 , 5 , 2\right) \cdot \left(- 3 , 1 , 7\right) = \left(- 8\right) \left(- 3\right) + \left(5\right) \left(1\right) + \left(2\right) \left(7\right)$

$= 24 + 5 + 14$

$= 43$ $\in \mathbb{R}$.