# If #A = <3 ,8 ,-1 >#, #B = <4 ,-7 ,-1 ># and #C=A-B#, what is the angle between A and C?

##### 1 Answer

Mar 4, 2016

#### Explanation:

To calculate the angle between 2 vectors

#ula " and "ulc#

use the following formula.

# costheta = (ula . ulc )/(|ula||ulc|) # where

#theta " is the angle between " ula " and " ulc# now C = A - B = (3,8,-1) - (4,-7,-1) = (-1,15,0)

#ula . ulc = (3,8,-1) . (-1,15,0)#

#= (3xx-1)+(8xx15)+(-1xx0) = -3 + 120 = 117 #

#|ula| = sqrt(3^2+8^2+(-1)^2) = sqrt(9+64+1) = sqrt74# and

#|ulc| = sqrt((-1)^2+15^2+0) = sqrt(1+225) = sqrt226#

#rArrtheta = cos^-1(117/(sqrt74xxsqrt226)) ≈ 0.44" radians "#