What is the dot product of <1,4,-7 > and <-1,6,2 >?

Sep 9, 2016

$< 1 , 4 , - 7 > \cdot < - 1 , 6 , 2 > = 9$

Explanation:

The dot product of two vectors is very easy!

Given,
$< {x}_{1} , {y}_{1} , {z}_{1} >$ and $< {x}_{2} , {y}_{2} , {z}_{2} >$,
$< {x}_{1} , {y}_{1} , {z}_{1} > \cdot < {x}_{2} , {y}_{2} , {z}_{2} >$
$= {x}_{1} \cdot {x}_{2} + {y}_{1} \cdot {y}_{2} + {z}_{1} \cdot {z}_{2}$

So, for our question,
$< 1 , 4 , - 7 > \cdot < - 1 , 6 , 2 >$
$= - 1 + 24 - 14 = 9 \square$