Let's begin by naming our vectors.
v#=<3,0>#
w#=<5,5>#
Dot product #-> v*w#
Angle between formula #->cos (theta)=(v*w)/(||v||*||w||)#
Solve for #theta#
#cos^-1(cos (theta))=cos^-1((v*w)/(||v||*||w||))#
#theta=cos^-1((v*w)/(||v||*||w||))#
Begin by finding the dot product of vectors #v and w# by adding the products of the horizontal and vertical components.
#theta=cos^-1(((3)(5)+(0)(5))/(||v||*||w||))#
#theta=cos^-1((15+0)/(||v||*||w||))#
Now find the magnitudes of both vectors
#theta=cos^-1((15)/(sqrt(9+0)*sqrt(25+25)))#
#theta=cos^-1((15)/(sqrt(9)*sqrt(50)))#
#theta=cos^-1((15)/(sqrt(3*3*5*5*2)))#
#theta=cos^-1((15)/(15sqrt(2)))#
#theta=cos^-1((1)/(sqrt(2)))#
#theta=pi/4#
