If #A = <4 ,2 ,5 >#, #B = <-8 ,2 ,6 ># and #C=A-B#, what is the angle between A and C?

1 Answer
Jim G.
Feb 10, 2016

1 radian

Explanation:

To calculate the angle between 2 vectors #ulacolor(black)(" and ") ulb#

the following is used:

#costheta =( ula . ulb)/(|ula| xx |ulb|) #

here C = A - B = (4,2,5) - (-8,2,6) = (12,0,-1)

#ula . ulc = (4,2,5) . (12,0,-1) = 48+0-5 = 43 #

#|ula| = sqrt(4^2+2^2+5^2) = sqrt45 #

and #|ulc| = sqrt(12^2+0^2+(-1)^2) = sqrt145#

# rArr costheta = 43/(sqrt45 xx sqrt145) #

# rArr theta = cos^-1 (43/((sqrt45 xx sqrt145))) = 1color(black)(" radian ")#

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