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Question
What is the formula to calculate the slope of plane?
The equation of a line in 2 dimension is ax+by=c, where -b/a is
the slope, or the tangent(of the angle) ,or ration change ,of the function y=-(a/b)x+c/b.
The equation of a plane in 3 dimensions is Ax + By + Cz = D.
To define a slope we need a specific angle of deviation ia a certain direction. Our plane function is z=-(A/C)x-(B/C)y+D/C.
-A/C is the tangent of the angle between our plane and the z-axis.
-B/C is the tangent of the angle between our plane and the y-axis. So in 3 dimension there 2 lopes or 2 angles for the plane.
Another way of regarding the "slope" of a plane is to write
down a unit vector which is perpendicular to it, called the normal
vector. It is given by (a*I + b*J + c*K)/sqrt(a^2+b^2+c^2), where
I,J, and K are the unit vectors in the x, y, and z directions. The
coefficients of I, J, and K in this expression are called the
direction cosines of the vector, because they are the cosines of the
angles between the vector and the x-, y-, and z-axes, respectively.
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Alon Mandes
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