If A = {2,-7 ,5}, B = {5,-7,4} and C = A - B, what is the angle between A and C?

1 Answer
Apr 5, 2016

alpha=90,02 ^o

Explanation:

"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