If #A = <2 ,4 ,-7 >#, #B = <3 ,8 ,2 ># and #C=A-B#, what is the angle between A and C?

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Answer 1 · 2016-05-13T15:21:21

56.78 degrees

C = A-B = < (2-3), (4-8), (-7-2)> = <-1,-4,-9>

||A||= #sqrt (2^2 +4^2+(-7)^2#= #sqrt69#

||C||= #sqrt((-1)^2 +(-4)^2 +(-9)^2) # =#sqrt98#

A.C= 2(-1) +4(-4) + (-7)(-9)= 45

If #theta# is the angle between A and C,

#costheta = 45/(sqrt69 sqrt98) #=0.5479

#theta#=56.78 degrees