# What is the dot product of <1,5,-3 > and <-1,4,2 >?

Nov 21, 2016

The dot product is $- 13$.
Let us consider $\left[1 , 5 , - 3\right]$ as $\vec{A} = \hat{i} + 5 \hat{j} - 3 \hat{k}$ and $\left[- 1 , 4 , 2\right]$ as $\vec{B} = - \hat{i} + 4 \hat{j} + 2 \hat{k}$.
The dot product of $\left[1 , 5 , - 3\right]$ and $\left[- 1 , 4 , 2\right]$ is $\vec{A} . \vec{B}$.
$\vec{A} . \vec{B} = {a}_{1} {b}_{1} + {a}_{2} {b}_{2} + {a}_{3} {b}_{3}$.
$\implies \vec{A} . \vec{B} = \left(1\right) \left(- 1\right) + \left(5\right) \left(4\right) + \left(- 3\right) \left(2\right) = - 13$.