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

Jul 26, 2018

The dot product is $= 23$

#### Explanation:

The dot product of $2$ vectors

$\vec{a} = < {x}_{1} , {x}_{2} , {x}_{3} >$

and

$\vec{b} = < {y}_{1} , {y}_{2} , {y}_{3} >$

is

$\vec{a} . \vec{b} = < {x}_{1} , {x}_{2} , {x}_{3} > . < {y}_{1} , {y}_{2} , {y}_{3} >$

$= {x}_{1} {y}_{1} + {x}_{2} {y}_{2} + {x}_{3} {y}_{3}$

Here the vectors are

$\vec{a} = < 2 , 4 , 7 >$ and $\vec{b} = < 1 , - 7 , 7 >$

The dot product is

$< 2 , 4 , 7 > . < 1 , - 7 , 7 > = 2 \cdot 1 + 4 \cdot \left(- 7\right) + 7 \cdot 7$

$= 2 - 28 + 49$

$= 23$