(a) (x-x_(1))/l=(y-y_(1))/m=(z-z_(1))/n=r , say, represent the equation of a line through the point (x_(1),y_(1),z_(1)) where l,m,n are d.c.'s of the line. (b) Angle between line and a plane ax+cz+d=0 , It is complement of the angle between line and normal to the plane :. " "cos(90^(@)-theta)=(al+bm+cn)/(sqrt(suma^(2)).sqrt(suml^(2))) (d)(i) Line is parallel to plane implies it is perpendiculer to normal :. " " al+bm+cn=0 (ii) Line is parallel to plane implies it is parallel to normal :. " "a/1=b/m=c/n (iii) Line to lie in the plane implies al+bm+cn=0 and ax_(1)+by_(1)+cz_(1)+d=0 The direction cosines of two lines at right angles are l_(1),m_(1),n_(1) and l_(2),m_(2),n_(2) . Then the d.c.'s of a line _|_ to both the given lines are

Comprehesion-I Let k be the length of any edge of a regular tetrahedron (all edges are equal in length). The angle between a line and a plane is equal to the complement of the angle between the line and the normal to the plane whereas the angle between two plane is equal to the angle between the normals. Let O be the origin and A,B and C vertices with position vectors veca,vecb and vecc respectively of the regular tetrahedron. The angle between any two faces is

Comprehesion-I Let k be the length of any edge of a regular tetrahedron (all edges are equal in length). The angle between a line and a plane is equal to the complement of the angle between the line and the normal to the plane whereas the angle between two plane is equal to the angle between the normals. Let O be the origin and A,B and C vertices with position vectors veca,vecb and vecc respectively of the regular tetrahedron. The angle between any edge and a face not containing the edge is