# What is the dot product of <-5,2,8 > and <-1,6,2 >?

Aug 22, 2017

The answer is $= 33$

#### Explanation:

The dot product of $2$ vectors, $\vec{a} = < {x}_{1} , {x}_{2} , {x}_{3} >$ and $\vec{b} = < {y}_{1} , {y}_{2} , {y}_{3} >$ is

$\vec{a} . \vec{b} = < {x}_{1} , {x}_{2} , {x}_{3} > . < {y}_{1} , {y}_{2} , {y}_{3} >$

$= {x}_{1} {y}_{1} + {x}_{2} {y}_{2} + {x}_{3} {y}_{3}$

Therefore,

$< - 5 , 2 , 8 > . < - 1 , 6 , 2 > = \left(- 5 \cdot - 1\right) + \left(2 \cdot 6\right) + \left(8 \cdot 2\right)$

$= 5 + 12 + 16 = 33$