If #A = <7 ,-8 ,-2 >#, #B = <4 ,-8 ,9 ># and #C=A-B#, what is the angle between A and C?

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Answer 1 · 2016-06-13T15:34:23

#69.6^@#

Given
#vecA=<7,-8,-2>#

#vecB=<4,-8,9>#
#=>vecA-vecB=<(7-4),(-8+8),(-2-9)>#
#=<3,0,-11>#

#|vecA|=sqrt(7^2+(-8)^2+(-2)^2)#
#=sqrt117#

#|vecC|=sqrt(3^2+(0)^2+(-11)^2)#
#=sqrt130#

Now if angle beween #vecA and vecC# be #theta# then

#costheta=(vecA*vecC)/(|vecA||vecC|)#

#=(7*3+(-8)*0+(-2)*(-11))/sqrt(117*130)#

#=43/(39sqrt10)#

#:.theta= 69.6^@#