# What is the dot product of <-6,1,0> and <2,7,5 > ?

Feb 3, 2016

$- 5$
To find the dot product of two column matrices $\left\{{a}_{1} , {b}_{1} , {c}_{1}\right\}$ and $\left\{{a}_{2} , {b}_{2} , {c}_{2}\right\}$ you multiply the equivalent components together as
$a \cdot b = \left({a}_{1} {a}_{2} + {b}_{1} {b}_{2} + {c}_{1} {c}_{2}\right)$
$< - 6 , 1 , 0 > \cdot < 2 , 7 , 5 > = \left(\left(- 6 \cdot 2\right) + 1 \cdot 7 + 0 \cdot 5\right)$
$= - 12 + 7 = - 5$