Find the cosine of the angle between the planes x + y + z = 0 and x + 2y + 5z = 3.
Homework Answers
A. B =
1 + 2 + 5 = (3)^0.5 x (30)^0.5 x cos(theta)
angle theta = 32.51 degreees
normal vectors to planes
(1,1,1) and (1,2,2)
use formula
VdotU=||V||*||U||*cos(pheta)
VdotU=1*1+1*2+1*2=5
||V||=sqrt(1^2+1^2+1^2=sqrt(3)
||U||=sqrt(1^2+2^2+2^2)=sqrt(9)
cos(pheta)=5sqrt(3)/9
pheta=15.8 degrees
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