The equation of a plane parallel to the plane $x - 2y + 2z - 5 = 0$ and at a unit distance from the origin is:

Let the plane $ax+by+cz+d=0$ bisect the line segment joining the points $P(4,-3,1)$ and $Q(2,3,-5)$ at right angles. If $a, b, c, d$ are integers,then the minimum value of $(a^{2}+b^{2}+c^{2}+d^{2})$ is

$P$ is a fixed point $(a, a, a)$ on a line through the origin equally inclined to the axes. Then,any plane through $P$ perpendicular to $OP$ makes intercepts on the axes,the sum of whose reciprocals is equal to:

The equation of the plane containing the lines $r = a_1 + \lambda a_2$ and $r = a_2 + \lambda a_1$ is

What is the equation of the plane passing through the intersection of the planes $x + 2y + 3z - 4 = 0$ and $4x + 3y + 2z + 1 = 0$,and also passing through the origin?

The plane which bisects the line segment joining the points $A(4, -2, 3)$ and $B(2, 4, -1)$ at right angles also passes through the point: