Let σ_{1}, σ_{2} be two planes; n_{1}, n_{2} be the unit normals to the planes σ_{1}, σ_{2} respectively.
Then (n_{1}, n_{2}), 180° – (n_{1}, n_{2}) are called the angles between two planes σ_{1} and σ_{2}.
If n_{1} and n_{2} are unit normals to the planes
r.n_{1} = d_{1} and r .n_{2} = d_{2} and θ is the angle between the normals, then
cos θ =
If the two planes are perpendicular to each other, then n_{1}.n_{2} = 0
If the two planes are parallel, then n_{1} is parallel to n_{2}.
Note:
(i) The component of b on a =
(ii) The component of a on b =
(iii) The orthogonal projection of b on a =
(iv) The orthogonal projection of a on b =