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

##### 1 Answer

Feb 19, 2016

2.82 radians

#≈ 162^@#

#### Explanation:

To calculate the angle between 2 vectors

#ula " and " ulc#

the following should be used.

#costheta = (ula . ulc)/(|ula||ulc|)# here C= A - B = (4,2,5) - (6,2,8) = (-2,0,-3)

now

#ula . ulc = (4,2,5) . (-2,0,-3)#

#=(4xx-2) + (2xx0) + (5xx-3) # = -8 + 0 -15 = - 23

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

#|ulc| = sqrt((-2)^2+0+(-3)^2) = sqrt(4+0+9) = sqrt13#

#rArr theta = cos^-1(-23/(sqrt45 xx sqrt13)) ≈ 2.82 " radians"#