# What is the angle between #< 6 , 1 , -4 > # and # < 2 , -3 , 2 > #?

##### 1 Answer

Jan 28, 2016

# 88^@ #

#### Explanation:

To find the angle between 2 vectors use the following formula :

# costheta =( veca.vecb)/((|veca| xx |vecb|) # where a and b represent the 2 vectors and

#theta color(black)(" the angle between them") # let

#veca = (6,1,-4) , vecb = (2 , - 3 , 2 ) # then

# veca . vecb = 12 - 3 - 8 = 1 # and

# |veca| = sqrt(6^2+1^2+(-4)^2) =sqrt(36+1+16) =sqrt53#

#|vecb| = sqrt(2^2+(-3)^2+2^2) = sqrt(4+9+4) = sqrt17 # hence

# costheta = 1/(sqrt53 xx sqrt17) #

# theta = cos^-1 (1/(sqrt901)) = 88^@#