# What is the dot product of <7,-8,1> and <4,-6,3 >?

Feb 3, 2016

$A . B = 28 + 48 + 3 = 79$
$A = 7 x - 8 y + z$
$B = 4 x - 6 y + 3 z$
$A . B = {A}_{x} \cdot {B}_{x} + {A}_{y} \cdot {B}_{y} + {A}_{z} \cdot {B}_{z}$
$A . B = 7 \cdot 4 + \left(\left(- 8\right) \cdot \left(- 6\right)\right) + 1 \cdot 3$
$A . B = 28 + \left(+ 48\right) + 3$
$A . B = 28 + 48 + 3 = 79$