# What is the dot product of <-1,1,2 >  and <-2,-8,-1 > ?

Feb 7, 2016

$a \cdot b = - 7$
$a = {a}_{_} i + {a}_{j} + {a}_{k}$
$b = {b}_{i} + {b}_{j} + {b}_{k}$
$a \cdot b = {a}_{i} \cdot {b}_{i} + {a}_{j} \cdot {b}_{j} + {a}_{k} \cdot {b}_{k}$
$a \cdot b = \left(- 1 \cdot - 2\right) + \left(1 \cdot - 8\right) + \left(2 \cdot - 1\right)$
$a \cdot b = 2 - 8 - 1$
$a \cdot b = - 7$