3.
Conditions for 2 planes to intersect in a line <ul><li>The line l </li></ul><ul><li>has a point that lies on both planes (thus, we may need to solve the equations), </li></ul><ul><li>is perpendicular to normal of plane 1, </li></ul><ul><li>is perpendicular to normal of plane 2, </li></ul><ul><li>so that direction vector is parallel to the vector product of the normals . </li></ul>
5.
Conditions for 3 planes to intersect in a line <ul><li>We start with 2 planes intersecting in a line l . </li></ul><ul><li>If l lies in plane 3, then </li></ul><ul><li>point on l lies on plane 3 (thus, point satisfies equation of plane 3 ), </li></ul><ul><li>direction vector of l is perpendicular to normal of plane 3 (thus, scalar product of direction vector and normal is zero ). </li></ul>
7.
3 planes do not intersect in a line <ul><li>We modify one of the earlier conditions. </li></ul><ul><li>We start with 2 planes intersecting in a line l . </li></ul><ul><li>If l does not lie in plane 3, then </li></ul><ul><li>point on l does not lie on plane 3 (thus, point does not satisfy equation of plane 3 ), </li></ul><ul><li>direction vector of l is still perpendicular to normal of plane 3. </li></ul>
Be the first to comment