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

Feb 28, 2016

For two vectors $< {x}_{1} , {y}_{1} , {z}_{1} >$ and $< {x}_{2} , {y}_{2} , {z}_{2} >$, the dot product is ${x}_{1} {x}_{2} + {y}_{1} {y}_{2} + {z}_{1} {z}_{2}$. In this case the dot product is $8 + 20 - 2 = 26$. The dot product of two vectors is a scalar.

Explanation:

Just showing it in a little more detail:

$< - 4 , 5 , - 2 > \cdot < - 2 , 4 , 1 > = \left(\left(- 4 \times - 2\right) + \left(5 \times 4\right) + \left(- 2 \times 1\right)\right)$
$= 8 + 20 - 2 = 26$