# How do you find the inner product <3,-2,4>*<1,-4,0>?

May 13, 2017

The inner product is $= 11$

#### Explanation:

The inner or dot product of 2 vectors

$\vec{A} = < {x}_{1} , {y}_{1} , {z}_{1} >$

And

$\vec{B} = < {x}_{2} , {y}_{2} , {z}_{2} >$

is

$\vec{A} . \vec{B} = < {x}_{1} , {y}_{1} , {z}_{1} > . < {x}_{2} , {y}_{2} , {z}_{2} >$

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

Here, we have

$< 3 , - 2 , 4 > . < 1 , - 4 , 0 > = \left(3 \cdot 1 + 2 \cdot 4 + 4 \cdot 0\right) = 3 + 8 = 11$