Given vectors u 6 4 and v 3 6 determine if the vectors are

Given vectors u = (-6, 4) and v = (3, 6) determine if the vectors are orthogonal. If they are not orthogonal, find the angle between the two vectors. The vectors are orthogonal. The vectors are not orthogonal. The angle between the two vectors is 49.4 degree. The vectors are not orthogonal. The angle between the two vectors is 79.0 degree. The vectors are not orthogonal. The angle between the two vectors is 82.9 degree.

Solution

u=<-6,4>

v=<3,6>

u.v=-6*3 +4*6

=6

since the dot product is not 0 . Therefore vectors are not orthogonal.

|u|=sqrt(36+16)=sqrt52

|v|=sqrt(9+36) =sqrt45

theta=cos^-1(6/(sqrt52*45))=82.9°