What is the equation of a plane with normal vector langleA,B,Crangle\\langle A, B, C \\ranglelangleA,B,Crangle through (x0,y0,z0)(x_0, y_0, z_0)(x0,y0,z0)?
A(x0)+B(y0)=C(z0)A(x_0) + B(y_0) = C(z_0)A(x0)+B(y0)=C(z0)
Ax+By+Cz=1Ax + By + Cz = 1Ax+By+Cz=1
A(x−x0)+B(y−y0)+C(z−z0)=0A(x-x_0) + B(y-y_0) + C(z-z_0) = 0A(x−x0)+B(y−y0)+C(z−z0)=0
Ax0+By0+Cz0=0A x_0 + B y_0 + C z_0 = 0Ax0+By0+Cz0=0