The Planes — Formula Sheet

ax + by + cz + d = 0

a(x - x₁) + b(y - y₁) + c(z - z₁) = 0

∣(x−x₁, y−y₁, z−z₁), (x₂−x₁, y₂−y₁, z₂−z₁), (x₃−x₁, y₃−y₁, z₃−z₁)∣ = 0

x/a + y/b + z/c = 1

If a plane passes through a point \( (x_1, y_1, z_1) \), its equation is \( a(x - x_1) + b(y - y_1) + c(z - z_1) = 0 \).

The general equation of a plane is $ax + by + cz + d = 0$.

The equation of a plane through $(x_1, y_1, z_1)$ is $a(x - x_1) + b(y - y_1) + c(z - z_1) = 0$.