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

Mar 17, 2018

#### Answer:

The dot product is $= 0$

#### Explanation:

The dot product of $2$ vectors $< {x}_{1} , {x}_{2} , {x}_{3} >$ and $< {y}_{1} , {y}_{2} , {y}_{3} >$ is

$< {x}_{1} , {x}_{2} , {x}_{3} > . < {y}_{1} , {y}_{2} , {y}_{3} > = {x}_{1} {y}_{1} + {x}_{2} {y}_{2} + {x}_{3} {y}_{3}$

Therefore,

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

$= 1 - 4 + 3$

$= 0$

As the dot product is $= 0$, the vectors are orthogonal.