Question

If `A = <4 ,7 ,2 >`, `B = <7 ,1 ,-4 >` and `C=A-B`, what is the angle between A and C?

Answer 1

Given

`A=<4,7.2> and B=<7,1,-4>`

`:.C=A-B=<-3,6,6>`

If the angle betwee A and C be `theta` then

`costheta=(A.C)/(abs(A)abs(B))`

`=(<4,7,2>.<-3,6.6>)/(sqrt(4^2+7^2+2^2)sqrt(3^2+6^2+6^2)`

`=(-12+42+12)/(sqrt69sqrt81)`

`=42/((sqrt69).9)=14/(3sqrt69)`

`=cos^-1(14/(3sqrt69))=55.81^@`