# How do you find the inner product and state whether the vectors are perpendicular given <-2,4,8>*<16,4,2>?

Oct 24, 2016

$= 0$ and perpendicular.

#### Explanation:

for two vectors

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

the inner (dot) product is calculated by

$\textcolor{b l u e}{\vec{a} . \vec{b} = {a}_{1} {b}_{1} + {a}_{2} {b}_{2} + {a}_{3} {b}_{3}}$

so $< - 2 , 4 , 8 > . < 16 , 4 , 2 >$

$= - 2 \times 16 + 4 \times 4 + 8 \times 2$

$= - 32 + 16 + 16$

$= 0$

For two vectors $\vec{a}$ and $\vec{b}$ to be perpendicular

$\textcolor{b l u e}{\vec{a} \bot \vec{b}} \iff \textcolor{b l u e}{\vec{a} . \vec{b} = 0}$

the two vectors in the question give inner product 0 $\therefore$ perpendicular.