If #A = <2 ,2 ,5 >#, #B = <5 ,-7 ,-1 ># and #C=A-B#, what is the angle between A and C?

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Answer 1 · 2017-12-17T19:10:16

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#A=((2),(2),(5))#

#B=((5),(-7),(-1))#

#C=((2),(2),(5))-((5),(-7),(-1))=((-3),(9),(6))#

Angle between vectors can be found by using the dot product:

#A*C=||A||*||C||cos(theta)#

#A*C=-6+18+30=42#

#||A||=sqrt((2)^2+(2)^2+(5)^2)=sqrt(33)#

#||C||=sqrt((-3)^2+(9)^2+(6)^2)=sqrt(126)=3sqrt(14)#

#42=sqrt(33)*3sqrt(14)costheta#

#costheta=42/(sqrt(33)*3sqrt(14))=>theta=arccos(42/(sqrt(33)*3sqrt(14)))=49.36^@#

2 .d.p.