Question

In R³, let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes P₁ : x + 2y – z + 1 = 0 and P₂ :2x – y + z – 1 = 0. Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane P₁. Which of the following points lie(s) on M?

Answer 1

Answer is (a) (0, 5/6, –2/3) & (b) (–1/6, –1/3,1/6)

Line L will be parallel to the line of intersection of P₁ and P₂.

Let a, b and c be the direction ratios of line L.

Thus, a + 2b – c = 0 and 2a – b + c = 0 

a:b: c ::1:–3,:– 5

The equation of the line L is

satisfy the line of projection, i.e. M.