I keep getting 70.528 degrees (arccos(64/192)) but when I insert that it comes out as wrong.
The normal vectors of the two planes are <8,8,8> and
<8,-8,8> respectively, or after dividing through by 8,
<1,1,1> and <1,-1,1>. So the angle theta between the
planes is such that
cos(theta) = (<1,1,1> dot <1,-1,1>) / (ll<1,1,1>ll*ll<1,-1,1>ll) =
(1 - 1 + 1) / (sqrt(3)*sqrt(3)) = 1/3.
Thus theta = cos^-1(1/3) = 70.529 degrees.
So I agree with you. I don't know what's going on. Could it be
a formatting issue or a significant figures issue?
These are parallel planes.
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The normal vectors of the two planes are <8,8,8> and
<8,-8,8> respectively, or after dividing through by 8,
<1,1,1> and <1,-1,1>. So the angle theta between the
planes is such that
cos(theta) = (<1,1,1> dot <1,-1,1>) / (ll<1,1,1>ll*ll<1,-1,1>ll) =
(1 - 1 + 1) / (sqrt(3)*sqrt(3)) = 1/3.
Thus theta = cos^-1(1/3) = 70.529 degrees.
So I agree with you. I don't know what's going on. Could it be
a formatting issue or a significant figures issue?
These are parallel planes.