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

$< 1 , 0 , - 2 > \cdot < - 1 , - 4 , 1 >$=$\left(1 \times \left(- 1\right) + 0 \times \left(- 4\right) + \left(- 2\right) \times 1\right) = - 3$
The dot product of vectors $< {x}_{1} , {y}_{1} , {z}_{1} >$ and $< {x}_{2} , {y}_{2} , {z}_{2} >$ is ${x}_{1} {x}_{2} + {y}_{1} {y}_{2} + {z}_{1} {z}_{2}$.
In this case, $< 1 , 0 , - 2 > \cdot < - 1 , - 4 , 1 >$=$\left(1 \times \left(- 1\right) + 0 \times \left(- 4\right) + \left(- 2\right) \times 1\right) = - 3.$