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

Author:
February 20th, 2023

##112.47^0##
C= A-B= <3,-1,3>– <2, -3, 5> = < 1,2,-2>
Angle between A and C would be given by ##cos theta=(A*C)/(|A| |C|)##
##cos theta = (3*1 +(-1)*2 + 3(-2))/ (sqrt(3^2 +(-1)^2 +3^2) sqrt(1^2+2^2 +(-2)^2))##
=##-5/(sqrt19 sqrt9)##= -0.3823
##theta= arccos-0.3823## =##112.47^0##

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