If #A = <4 ,2 ,-5 >#, #B = <6 ,4 ,9 ># and #C=A-B#, what is the angle between A and C?

1 Answer
Feb 22, 2016

# 2.91" radians" , ( 166.8^@)#

Explanation:

To calculate the angle between 2 vectors #ula" and" ulc#

use: #costheta =( ula . ulc)/(|ula||ulc|) #

where #theta" is the angle between" ulaand" ulc#

here C = A - B = (4,2,-5) - (6,4,9) = (-2,-2,4)

hence: #ula . ulc = (4,2,-5) . (-2,-2,4)#

#= (4xx-2)+(2xx-2) +(-5xx4) = -8-4-20 = -32#

#|ula| = sqrt(4^2+2^2+(-5)^2) = sqrt(16+4+25) = sqrt45#

and#|ulc| = sqrt((-2)^2+(-2)^2+4^2) = sqrt(4+4+16) = sqrt24#

#rArr theta = cos^-1((-32)/(sqrt45xxsqrt24)) ≈ 2.91" radians"#