Consider the vectors 6i 2i 3j Find the dot product of the t

Consider the vectors. 6i, 2i + 3j Find the dot product of the two vectors. Find the angle between the two vectors. (Round your answer to the nearest minute.)

Solution

6i,2i+3j

6i=6i+0j,2i+3j

Dot product is (6*2)+(0*3)

=12

And a.b= I aI * IbI cos theta

And we have a.b=12

And IaI=sqrt(6^2+0^2)=6

And IbI= sqrt(2^2+3^2)=sqrt 13

Therefore 12=6* sqrt 13 cos theta

cos theta=12/(6*sqrt13)=.5547

Taking inverse on both sides

co^-1(cos theta)=cos^-1.5547

theta= 56.31 degree

theta= 56 degree 19 minutes