Find the angle theta between the vectors and theta 224 in r

Find the angle theta between the vectors and theta = 2.24 (in radians)

Solution

v1 = < -4,-4,1> ; v2 = <2,5,4>

dot product : v1.v2 = -8 -20+4 = -24

||v1|| = sqrt(4^2 + 4^2+1> = sqrt33

||v2|| = sqrt(2^2 + 5^2 + 4^2) = sqrt(45)

costheta = v1*v2/||v1||||v2||

= -24/sqrt(33*45)

= -24/38.535 =

theta = pi -0.898 = 2.243