# How do you find the inner product and state whether the vectors are perpendicular given <7,2>*<0,-2>?

Jun 29, 2016

$\setminus < 7 , 2 > \cdot < 0 , - 2 > = - 4$

they are not perpendicular

#### Explanation:

the inner or dot product in 2D is

$\setminus \vec{A} \cdot \setminus \vec{B} = \setminus < {A}_{x} , {A}_{y} > \cdot < {B}_{x} , {B}_{y} > = {A}_{x} {B}_{x} + {A}_{y} {B}_{y}$

here you have

$\setminus < 7 , 2 > \cdot < 0 , - 2 > = 7 \left(0\right) + 2 \left(- 2\right) = - 4$

they are not perpendicular as the dot product is not zero

to understand this, another definition of the dot prod is $\setminus \vec{A} \cdot \setminus \vec{B} = | \vec{A} | \setminus | \vec{B} | \setminus \cos \alpha$ where $\alpha$ is the angle between the direction of the vectors

if $\alpha = \frac{\pi}{2} , \frac{3 \pi}{2} , \ldots . ,$ then $\cos \alpha = 0$ and the dot product is non-trivially zero