If #A = <6 ,1 ,5 >#, #B = <4 ,6 ,-1 ># and #C=A-B#, what is the angle between A and C?
1 Answer
Feb 11, 2016
0.95 radians
Explanation:
To find the angle between 2 vectors
# ulacolor(black)(" and ") ulc#
# costheta =( ula .ulc)/(|ula| |ulc|) # where
# thetacolor(black)(" is the angle between them ")# here C = A- B = (6,1,5) - (4,6,-1 ) = (2,-5,6 )
now
# ula . ulc = (6,1,5) . (2,-5,6) =12-5+30 = 37 #
#|ula| = sqrt(6^2+1^2+5^2) = sqrt(36+1+25) = sqrt62 # and
# |ulc| = sqrt(2^2+(-5)^2 +6^2) = sqrt(4 + 25 + 36) = sqrt65# hence
# costheta = 37/(sqrt62 xx sqrt65) #
# rArr theta = cos^-1(37/(sqrt62 xx sqrt65)) = 0.95color(black)(" radians ")#
