If #A = <2 ,4 ,-7 >#, #B = <3 ,5 ,2 ># and #C=A-B#, what is the angle between A and C?

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Answer 1 · 2018-04-30T12:29:22

The angle between #vec A and vec C# is #41.13^0#

#vec C=vec A- vec B = (< 2,4,-7 >) - (< 3,5,2 >)#

#=(< 2-3,4-5,-7-2 >) =< -1,-1,-9 >#

#vec A =<2,4, -7> and vec C =<-1,-1,-9> ; theta#

be the angle between them ; then we know

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

#=((2* -1)+(4* -1)+(-7* -9))/(sqrt(2^2+4^2+(-7)^2)* (sqrt((-1)^2+(-1)^2+(-9)^2))#

#= 57/(sqrt69*sqrt83)=57/75.68. ~~0.7532#

#:. theta=cos^-1(0.7532)~~41.13^0#

The angle between #vec A and vec C# is #41.13^0# [Ans]