If #A = <3 ,-1 ,8 >#, #B = <2 ,-3 ,5 ># and #C=A-B#, what is the angle between A and C?

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Answer 1 · 2016-01-29T15:56:53

#theta#= 39.10 degrees approx

C= A-B will be < 1,2,3>. Assuming #theta# to be the angle between A and C, IAI ICI cos #theta# = A.C

IAI = #sqrt (3^2 +(-1)^2 +8^2) = sqrt74#
ICI= #sqrt(1^2 +2^2 +3^2) = sqrt 14#

A.C = 3(1) +(-1)(2)+8(3) = 25

Hence Cos#theta= 25/(sqrt14 sqrt74)#= 0.776

#theta#= 39.10 degrees approx