( iv) Four points A( x1, y1, z1), B( x2, y2, z2), C( x3, y3, z3) and D( x4, y4, z4) are coplanar if and only if
( v) Equation of the plane containing two coplanar lines
Angle between Two Planes
The angle between two planes is defined as the angle between the normal to them from any point.
Thus, the angle between the two planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0
is equal to the angle between the normals with direction cosines ± a1 / √Σ a 2 1, ± b1 / √Σ a 2 1, ± c1 / √Σ a 2 1
and ± a2 / √Σ a 2 2, ± b2 / √Σ a 2 2, ± c2 / √Σ a 2 2
If θ is the angle between the normals, then cos θ = ± a1a2 + b1b2 + c1c2 / √a 2 1 + b 2 1 + c 2 1 √a 2 2 + b 2 2 + c 2 2