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# How to solve problems involving relationships between planes

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### Transcript of "How to solve problems involving relationships between planes"

1. 1. Eton Education Centre www.etontuition.com 63853133 How to solve problems involving relationships between planes? By Wee WS wenshih.wordpress.com
2. 2. Consider this example
3. 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>
4. 4. Approach to (i)
5. 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>
6. 6. Approach to (ii)
7. 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>
8. 8. Approach to (iii)