#"Strategy...."#
#1 diamond" find " C=A-B #
#2 diamond" find || A|| (magnitude of A)" #
#3 diamond" find ||C|| (magnitude of C)"#
#4 diamond" find A.C (dot product of A and C)"#
#5 diamond" use A.C=||A||.||C||. cos" theta " (dot product formula)"#
#1diamond" ......................................................"#
#A_x=3" ; "A_y=2" ; "A_z=5#
#B_x=5" ; "B_5=-7" ; "B_z=8#
# C= < (A_x-B_x),(A_y-B_y),(A_z-B_z) >#
#C= < (3-5),(2+7),(5-8)#
#"we obtain :"#
#C= < -2,9,-3>#
#2diamond" ........................................................"#
#||A||=sqrt(A_x^2+A_y^2+A_z^2)=sqrt(3^2+2^2+5^2)=sqrt38#
#3diamond" .........................................................."#
#||C||=sqrt(c_x^2+C_y^2+C_z^2)=sqrt((-2)^2+9^2+(-3)^2)#
#||C||=sqrt(4+81+9)=sqrt94#
#4diamond" ..........................................................." #
#A*C=A_x*C_x+A_y*C_y+A_z*C_z#
#A*C=3*(-2)+2*9+5*(-3)=-6+18-15#
#A*C=-3#
#5diamond" ............................................................"#
#-3=sqrt38*sqrt94*cos theta#
#cos theta=-3/(sqrt(38*94))#
#cos theta=-3/(59.766)#
#cos theta=0.0501957635#
#theta=87.12#
