Question

If the foot of the perpendicular from the point A(-1, 4, 3) on the plane P : 2x + my + nz = 4, is (-2 , 7/2 , 3/2), then the distance of the point A from the plane P, measured parallel to a line with direction ratios 3, -1, -4, is equal to :

(A) 1 

(B) √26 

(C) 2√2 

(D) √14

Answer 1

Correct option is (B) √26 

Let B be foot of ⟂ coordinaters of B = (-2 , 7/2 , 3/2)

Direction ratio of line AB is < 2,1,3 > so 

m = 1 , n = 3

So equation of AC is x+1/3 = y-4.-1 = z-3/-4 = λ

So point C is (3λ - 1, - λ+ 4, -4λ + 3). But C lies on the plane, so