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Z and ZX-planes :, , ine f a point on XY i} |, Coordinates 0 p ee a, , XY-plane will be of, yZ-plane is of the form (0,8, Y)., ZX-plane is of the form (Q, 0, Y)., , (1) Coordinates of a point in, (2) Coordinates of a point in, (3) Coordinates of a point in, , 26.9., , (1) (a) Two intersecting lines are always coplanar., , drawn through two intersecting lines. 3 4 7, ree non-collinear points, (b) One and only one plane can be drawn through three points., , 9a ove ine ¢ 2 Vive, (c) One and only one plane can be drawn through a given line and a given, , One and only one plane can be, , point not on the given line., (d) Two parallel lines of space are always coplanar., (2) Two lines of space may not be coplanar. Such lines are called skew lines., , (3) (a) Ifa line is perpendicular to two intersecting lines, then it is perpendicular, , to their plane., (b) Ifa line is perpendicular to a plane, then it is perpendicular to every line, of that plane., , Worked Out Examples, , TYPE |, , , , , Problems based on coordinates of a point., , WORKING RULE : Use the following informations whichever are required, , Coordinates of any point on x-axis is (x, 0, 0) ‘On, Coordinates of any point on yaxis is (0, y, 0) J, Coordinates of any point on z-axis is (0, 0, z), , Coordinates of any point on XY-plane is (x, y, 0), Coordinates of any point on ¥Z-plane is (0, y, z), Coordinates of any point on ZX-plane is (x, 0, z), , DAR WH, , 7. Distance of point (a,b,c) from xaxis =e +2, , 8. Distance of point (a,b,c) from yaxis =yq? + ¢?, , 9. Distance of point (a,b,c) from Z-axis alae +b?, , 10. If a point moves parallel to +, 11. If a point moves parallel, , i a, , axis, then its yand z coordinates re nal, to XY-plane, then its z coordinate”, , constant.