The equation of line of intersection of planes 4x + 4y - 5z = 12, 8x + 12y - 13z = 32can be written as :
The equation of the plane, which makes with co-ordinate axes, a triangle with its centroid is :
C.
Let the vertices of triangle are A (a, 0, 0), B (0, b, 0) and C (0, 0, c) and the equation of plane is
which is the equation of required plane.
A variable plane moves so that sum of the reciprocals of its intercepts on the co-ordinate axes is 1/2. Then the plane passes through :
(- 1, 1, 1)
(2, 2, 2)
(0, 0, 0)
The direction cosines l, m, n of two lines are connected by the relations l + m + n = 0, lm = 0, then the angle between them is :
0