# What is the angle between #<-3,2,6 > # and #<5,0,-5> #?

##### 1 Answer

Feb 20, 2016

2.71 radians ≈

#### Explanation:

To calculate the angle between 2 vectors

# ula " and" ulb#

use the following formula.

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

#ula = (-3,2,6) " and " ulb = (5,0,-5)# hence

#ula . ulb = (-3,2,6) . (5,0,-5)#

# = (-3xx5) + (2xx0) + (6xx-5) # = -15 + 0 - 30 = - 45

#|ula| = sqrt((-3)^2+2^2+6^2) = sqrt(9+4+36) = sqrt49 = 7 #

#|ulb| = sqrt(5^2+0+(-5)^2) = sqrt(25+0+25) = sqrt50#

#rArrtheta= cos^-1((-45)/(7xxsqrt50))= 2.71" radians" #