"a) find C=A-B"
C=(A_x-B_x),(A_y-B_y),(A_z-B_z)
C=(2-5),(-7+7),(5-4)
C={-3,0,1}
"b) find the magnitude of A and C:"
||A||=sqrt(A_x^2+A_y^2+A_z^2)
||A||=sqrt(2^2+(-7)^2+5^2)=sqrt(4+49+25)=sqrt78
||C||=sqrt(C_x^2+C_y^2+C_z^2)
||C||=sqrt((-3)^2+0^2+1^2)=sqrt(9+0+1)=sqrt10
"c) find dot product of A.C"
A*C=A_x*C_x+A_y*C_y+A_z*C_z
A*C=2*(-3)+(-7)*0+5*1
A*C=-6+0+5=-1
"d) use the dot product formula"
A.C=||A||*||C||*cos alpha
A*C=-1
||A||=sqrt78
||C||=sqrt10
-1=sqrt78*sqrt10*cos alpha
cos alpha=-1/(sqrt78*sqrt10)
cos alpha=-1/sqrt780
cos alpha=-1/(27,93)
alpha=90,02 ^o