# What is the dot product of <-4,0,-2 > and <3,-9,1>?

Jun 1, 2018

The answer is $= - 14$

#### Explanation:

The dot product of $2$ vectors

$\vec{x} = < a , b , c >$

and

$\vec{y} = < d , e , f >$

is

$\vec{x} . \vec{y} = < a , b , c > . < d , e , f > = a d + b e + c f$

Therefore,

$< - 4 , 0 , - 2 > . < 3 , - 9 , 1 > = \left(- 4\right) \cdot \left(3\right) + \left(0\right) \cdot \left(- 9\right) + \left(- 2\right) \cdot \left(1\right)$

$= - 12 + 0 - 2$

$= - 14$