Mark against the correct answer in each of the following:
The foot of the perpendicular from the point A(7, 14, 5) to the plane 2x + 4y – z = 2 is
Given: Perpendicular dropped from A(7, 14, 5) on to the plane 2x + 4y – z = 2
To find: co-ordinates of the foot of perpendicular
Formula Used: Equation of a line is
Where b1:b2:b3 is the direction ratio and (x1, x2, x3) is a point on the line.
Explanation:
Let the foot of the perpendicular be (a, b, c)
Since this point lies on the plane,
2a + 4b – c = 2 … (1)
Direction ratio of the normal to the plane is 2 : 4 : -1
Direction ratio perpendicular = direction ratio of normal to the plane
So, equation of the perpendicular is
Since (a, b, c) is a point on the perpendicular,
(7, 14, 5) is a point on the perpendicular.
So, a = 7 - 2λ, b = 14 – 4λ, c = 5 + λ
Substituting in (1),
14 – 4λ + 56 – 16λ – 5 - λ = 2
21λ = 70 – 7 = 63
λ = 3
Therefore, foot of the perpendicular is (1, 2, 8)