# What is the angle between #<-3 , -5 ,1 > # and # < -4, 7 ,-2 > #?

##### 1 Answer

Feb 19, 2016

2.1 radians ≈

#120^@ #

#### Explanation:

To calculate the angle between 2 vectors

#ula " and" ulb #

use the following formula.

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

where# theta " is the angle between the vectors"# here let

#ula =(-3 , -5 , 1 ) " and " ulb = (-4 ,7 , -2)# hence

#ula . ulb = (-3,-5,1) . (-4,7,-2) # =(

#-3xx-4) + (-5xx7) + (1xx-2) # = 12-35-2 = -25

#|ula| = sqrt((-3^2)+(-5)^2+1^2) = sqrt(9+25+1) = sqrt35# and

#|ulb| = sqrt((-4)^2+7^2+(-2)^2) = sqrt(16+49+4) = sqrt69#

#rArr cos^-1((-25)/(sqrt35 xx sqrt69)) ≈ 2.1 " radians"#