The shortest distance from the origin to a variable point on the sphere $(x-2)^2+(y-3)^2+(z-6)^2=1$ is

If $A(3, -2, 2)$ and $B(2, \lambda+1, 5)$ are the end points of the diameter of a circle and the point $P(5, 6, -1)$ lies on the circle,then $\lambda=$

The shortest distance from the plane $12x + 4y + 3z = 327$ to the sphere $x^2 + y^2 + z^2 + 4x - 2y - 6z = 155$ is

How many distinct spheres of radius $r$ can be drawn such that they touch all three coordinate planes?

The ratio in which the sphere ${x^2} + {y^2} + {z^2} = 504$ divides the line segment $AB$ joining the points $A(12, -4, 8)$ and $B(27, -9, 18)$ is given by

The radius of the circle in which the sphere $x^2 + y^2 + z^2 + 2x - 2y - 4z - 19 = 0$ is cut by the plane $x + 2y + 2z + 7 = 0$ is