For a point object,which of the following always produces a virtual image in air?

$A$ ray of light is incident on a convex mirror along a vector $3\hat i + 4\hat j + 12\hat k$. The normal to the convex mirror at the point of incidence is along $3\hat i + 4\hat j$. The unit vector along the reflected ray is:

Assertion $(A):$ The relation among $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason $(R):$ The laws of reflection are strictly valid for plane surfaces but not for large spherical surfaces.

Draw the ray diagram when an object is placed between the focus $(F)$ and the pole $(P)$ of a concave mirror.

An object of length $f/3$ is placed on the principal axis of a concave mirror of focal length $f$. The image of the end of the object farthest from the mirror is formed at the same position. Find the length of the image.

$A$ virtual image three times the size of the object is obtained with a concave mirror of radius of curvature $36 \ cm$. The distance of the object from the mirror is ........ $cm$.