Find the coordinates of the foot of the perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, -1, 3) and C(2, -3, -1).
Find the coordinates of the foot of the perpendicular drawn from the point A(1, 8, 4) to the line joining the points B(0, -1, 3) and C(2, -3, -1).

Find the coordinates of the foot of the perpendicular drawn from the point to the line joining the points and Given: perpendicular drawn from point to line joining points and To find: foot of perpendicular
Formula Used: Equation of a line is
Vector form: Cartesian form: where is a point on the line and with being the direction ratios of the line.
If 2 lines of direction ratios and are perpendicular, then Explanation: is a point on the line.
Therefore, Also direction ratios of the line are Any point on the line will be of the form So the foot of the perpendicular is of the form The direction ratios of the perpendicular is

From the direction ratio of the line and the direction ratio of its perpendicular, we have
So, the foot of the perpendicular is 