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

The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x - y + 5z - 3 = 0$ are $ . . . . . . $.

The plane passing through the point $(4, -1, 2)$ and parallel to the lines $\frac{x + 2}{3} = \frac{y - 2}{-1} = \frac{z + 1}{2}$ and $\frac{x - 2}{1} = \frac{y - 3}{2} = \frac{z - 4}{3}$ also passes through the point

The vector equation of the plane passing through the point $A(1, 2, -1)$ and parallel to the vectors $2 \hat{i} + \hat{j} - \hat{k}$ and $\hat{i} - \hat{j} + 3 \hat{k}$ is

In space,the equation $by + cz + d = 0$ represents a plane perpendicular to the

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