Question
Find the coordinates of the foot of perpendicular drawn from the point A (1, 2, 1) to the line
Solution
The equation of line BC
or
or
Any point D on it is
(4 k + 1, 4, – 2 k + 6)
Let D be foot of perpendicular from A on BC.
Direction ratios of AD are
4 k + 1–1, 4 – 2, – 2 k + 6 – 1 i.e., 4 k , 2, – 2 k + 5
Direction ratios of BC are 4, 0, – 2
Since AD is perpendicular to BC
∴ (4 k) (4) + (2) (0) + (– 2 k + 5) (–2) = 0
