Question
Find the coordinates of the foot of perpendicular drawn from the point A (1, 2, 1) to the line joining B (1, 4, 6) and (5, 4, 4). Also find the perpendicular distance of A from line BC.
Solution
The equation of line through B (1, 4, 6) and C (5, 4, 4) is
or
Any point D on it is (4 k+1 , 4, –2 k + 6)
Let D be foot of perpendicular from A on BC.
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
⊥ distance of A from BC = distance AD
