Three Dimensional Geometry
The equation of the plane containing the line 2x−5y+z=3;x+y+4z=5, and parallel to the plane, x+3y+6z=1, is :
Prove that the lines 1x=2y−2=3z+3 and 2x−2=3y−6=4z−3 are coplanar. Also find the equation of the plane containing these lines.
Find the vector and Cartesian equations of a plane which is at a distance of 5 units from the origin and which has 3i^−2j^+6k^ as the unit vector normal to it.
Find the equation of the plane through the intersection of the planes 3x−4y+5z=10 and 2x+2y−3z=4 and parallel to the line x=2y=3z