List of top Mathematics Questions on Co-ordinate Geometry asked in UP Board XII

If the lines \[ \frac{x - 1}{3} = \frac{y - 2}{2k} = \frac{z - 3}{2} \quad {and} \quad \frac{x - 1}{3k} = \frac{y - 1}{1} = \frac{z - 6}{-5} \] are perpendicular, find the value of \( k \).

Prove that the radius of the right circular cylinder of maximum curved surface inscribed in a cone is half of the radius of the cone.