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

1 Answer
Jun 29, 2016

Answer:

#\< 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