List of top Mathematics Questions on Distance of a Point From a Line asked in CBSE CLASS XII

Find the foot of the perpendicular from the point \( (0, 2, 3) \) on the line \( \frac{-x-3}{-5} = \frac{1-y}{-2} = \frac{3z+12}{9} \) and hence find the length of the perpendicular.

Find the foot of the perpendicular from the point \( (0, 2, 3) \) on the line \( \frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3} \) and hence find the length of the perpendicular.

The length of perpendicular drawn from the point \( (3, 4, 2) \) on the line \( \frac{x}{0} = \frac{y}{0} = \frac{z}{1} \) is

Find the coordinates of the foot of the perpendicular drawn from the origin \((0, 0, 0)\) to the straight line given by the equations \( \frac{x-2}{1} = \frac{y+1}{1} = \frac{z-3}{-1} \).

Find the point on the line \( \frac{x-1}{3} = \frac{y+1}{2} = \frac{z-4}{3} \) at a distance of \( \sqrt{2} \) units from the point \( (-1, -1, 2) \).

Find the foot of the perpendicular drawn from the point \( (1, 1, 4) \) on the line \( \frac{x+2}{5} = \frac{y+1}{2} = \frac{z-4}{-3} \).

Find the point on the line \( \frac{x-1}{3} = \frac{y+1}{2} = \frac{z-4}{3} \) at a distance of \( \sqrt{2} \) units from the point \( (-1, -1, 2) \).