Line of Intersection of Two Planes Calculator

Planes use ax+by+cz=d. Their intersection is (x,y,z)=(x0,y0,z0)+t(dx,dy,dz) for any real t. Parallel or coincident planes are excluded.

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Result

Enter your values and run the tool to see your result.

Check the units, enter your values, and run the tool. Results follow the assumptions and method below.

Point on line x((d1*b2-d2*b1)*(a1*b2-b1*a2)-(d1*c2-d2*c1)*(c1*a2-a1*c2))/((b1*c2-c1*b2)^2+(c1*a2-a1*c2)^2+(a1*b2-b1*a2)^2)

Point on line y((d1*c2-d2*c1)*(b1*c2-c1*b2)-(d1*a2-d2*a1)*(a1*b2-b1*a2))/((b1*c2-c1*b2)^2+(c1*a2-a1*c2)^2+(a1*b2-b1*a2)^2)

Point on line z((d1*a2-d2*a1)*(c1*a2-a1*c2)-(d1*b2-d2*b1)*(b1*c2-c1*b2))/((b1*c2-c1*b2)^2+(c1*a2-a1*c2)^2+(a1*b2-b1*a2)^2)

Direction vector xb1*c2-c1*b2

Direction vector yc1*a2-a1*c2

Direction vector za1*b2-b1*a2