SOLUTION: Find the angle between the planes 3x-y+z-5=0 and x+2y+2z+2=0.

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Question 942470: Find the angle between the planes 3x-y+z-5=0 and x+2y+2z+2=0.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the normal of each plane, then use the dot product.
N%5B1%5D=(3,-1,1)
N%5B2%5D=(1,2,2)
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N%5B1%5D%2AN%5B2%5D=abs%28N%5B1%5D%29abs%28N%5B2%5D%29cos%28theta%29
abs%28N%5B1%5D%29=sqrt%283%5E2%2B%28-1%29%5E2%2B1%5E2%29=sqrt%289%2B1%2B1%29=sqrt%2811%29
abs%28N%5B2%5D%29=sqrt%281%5E2%2B2%5E2%2B2%5E2%29=sqrt%281%2B4%2B4%29=sqrt%289%29=3
N%5B1%5D%2AN%5B2%5D=3%281%29%2B%28-1%29%282%29%2B1%282%29=3-2%2B2=3
So then,
3=sqrt%2811%29%2A3%2Acos%28theta%29
cos%28theta%29=1%2Fsqrt%2811%29
theta=72.5degrees