Question

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

Answer 1

`\< 7 , 2 >* < 0, -2 > = -4`

they are not perpendicular

Explanation:

the inner or dot product in 2D is

`\vec A * \vec B = \< A_x , A_y >* < B_x, B_y > = A_x B_x + A_y B_y`

here you have

`\< 7 , 2 >* < 0, -2 > = 7(0) + 2(-2) = -4`

they are not perpendicular as the dot product is not zero

to understand this, another definition of the dot prod is `\vec A * \vec B = |vec A| \ |vec B| \ cos alpha` where `alpha` is the angle between the direction of the vectors

if `alpha = pi/2, (3pi) /2,....,` then `cos alpha = 0` and the dot product is non-trivially zero