If A = <2 ,3 ,-1 >, B = <6 ,1 ,2 > and C=A-B, what is the angle between A and C?
1 Answer
Apr 8, 2016
- The angle between
vecA andvecC =90
Explanation:
C=A-B=<-4,2,-3> - If you consider that the vectors are in rectangular form (the vectors' tail is on the origin), the vector difference between two vectors
A-B goes from the head ofvecA to the to the head ofvecB forming a triangleABC . - By finding the magnitude of the vectors, you can find the sine of the angle between to
vecA andvecC (angleAC) . -
|A|=sqrt(2^2+3^2+(-1)^2)=3.74
|B|=sqrt(6^2+1^2+2^2)=6.40
|C|=sqrt((-4)^2+2^2+(-3)^2)=5.39 -
Using the sine rule:
|A|/(sinangleBC)=|C|/(sinangleAB)=|B|/(sinangleAC)
3.74/(sinangleBC)=5.39/(sinangleAB)=6.40/(sinangleAC) -
Doing the algebra:
angleAB=180-(angleAC+angleBC)
sinangleAB=sin(180(angleAC+angleBC))=sin(angleAC+angleBC)
- The angle between
vecA andvecC =90