# What is the dot product of <-6,4,2 >  and <7,1,0 > ?

Apr 20, 2018

The dot product is $= - 38$

#### Explanation:

The dot product of $2$ vectors

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

and

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

is

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

$= \left(a \times d\right) + \left(b \times e\right) + \left(c \times f\right)$

So,

The dot product is

$= < - 6 , 4 , 2 > . < 7 , 1 , 0 >$

$= \left(- 6 \times 7\right) + \left(4 \times 1\right) + \left(2 \times 0\right)$

$= - 42 + 4 + 0$

$= - 38$