     1. Chapter 11 Class 12 Three Dimensional Geometry
2. Serial order wise
3. Miscellaneous

Transcript

Misc 17 Find the equation of the plane which contains the line of intersection of the planes . ( + 2 + 3 ) 4 = 0 , . (2 + ) + 5 = 0 and which is perpendicular to the plane . (5 + 3 6 ) + 8 = 0 . Equation of a plane passing through the intersection of the places A1x + B1y + C1z = d1 and A2x + B2y + C2z = d2 is (A1x + B1y + C1z d1) + (A2x + B2y + C2z d2) = 0 Converting equation of planes to Cartesian form to find A1, B1, C1, d1 & A2, B2, C2, d2 Equation of plane is (A1x + B1y + C1z d1) + (A2x + B2y + C2z = d2) = 0 Putting values (1x + 2y + 3z 4) + ( 2x 1y + 1z 5) = 0 (1 2 ) x + (2 )y + (3 + ) z + ( 4 5 ) = 0 Now, the plane is perpendicular to the plane .(5 + 3 6 ) + 8 = 0 So, normal to plane will be perpendicular to normal of .(5 + 3 6 ) + 8 = 0 Now, .(5 + 3 6 ) + 8 = 0 .(5 + 3 6 ) = 8 .(5 + 3 6 ) = 8 .( 5 3 + 6 ) = 8 Finding direction cosines of & Since, is perpendicular to 1 2 + b1 b2 + c1 c2 = 0 (1 2 ) 5 + (2 ) 3 + (3 + ) 6 = 0 5 + 10 6 + 3 + 18 + 6 = 0 19 + 7 = 0 = Putting value of in (1), (1 2 ) x + (2 )y + (3 + ) z + ( 4 5 ) = 0 1 2 7 19 x + 2 7 19 y + 3+ 7 19 z + 4 5 7 19 = 0 1 + 14 19 x + 2 + 7 19 y + 3 7 19 z + 4 + 35 19 = 0 33 19 x + 45 19 y + 50 19 z 41 19 = 0 1 19 (33x + 45y + 50z 41) = 0 33x + 45y + 50z 41 = 0 Therefore, the equation of the plane is 33x + 45y + 50z = 41.

Miscellaneous 