What is the angle between #<7,-3,1 > # and #< -2,8,-5 >#?

1 Answer
Jim G.
Feb 25, 2016

#2.19" radians " (125.5^@)#

Explanation:

To calculate the angle between 2 vectors #ula " and " ulb " use"#

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

let #ula = (7,-3,1) " and " ulb = (-2,8,-5) #

(1) calculate the#color(blue)" the dot product "ula . ulb "#

#ula . ulb = (7,-3,1) . (-2,8,-5) #

#= (7xx-2) + (-3xx8) + (1xx-5) = -14-24-5 = -43 #

(2) calculate the#color(blue) " magnitudes of " ula , ulb#

#|ula| = sqrt(7^2+(-3)^2+1^2) =sqrt(49+9+1) = sqrt59#

#|ulb| = sqrt((-2)^2+8^2+(-5)^2)=sqrt(4+64+25) =sqrt93#

#rArr theta = cos^-1((-43)/(sqrt59xxsqrt93)) = 2.19 " radians "#

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