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

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 \( (-1, -1, 2) \).