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JEE Main20253 Apr 2025Morning ShiftMathematicsThree Dimensional GeometryActual

Let a line passing through the point (4,1,0) intersect the line L₁ ; x-1 2 = y-2 3 = z-3 4 at the point A ( , , ) and the line L₂: x-6=y=-z+4 at the point B(a, b, c) . Then | array lll 1 & 0 & 1 & & a & b & c array | is equal to

Options

  1. A8
  2. B16
  3. C12
  4. D6

Correct answer

A. 8

Step-by-step solution

aligned & L₁= x-1 2 = y-2 3 = z-3 4 =p & L₂= x-6 1 = y 1 = z-4 -1 =q & A(2 p+1,3 p+2,4 p+3) & B(q+6, q, 4-q) & D.R. of P A=2 p-3,3 P+1,4 p+3 & D.R. of P B=q+2, q-1,4-q & 2 p-3 q+2 = 3 p+1 q-1 = 4 p+3 4-q aligned aligned & 2 p q-2 p-3 q+3=3 p q+6 p+q+2 & pq + rp +4 q -1=0 & 12 p-3 p q+4-q=4 p q+3 q-4 p-3 & 7 p q-16 p+4 q-7=0 & 8 p-2 p q-12+3 q=4 p q+8 p+3 q+6 & 6 pq =-18 pq =-3 & 8 p+4 q=4 2 p+q=1 & -21-16 p+4 q-7 4 p-q=-7 & 16 p -4 q =-28 p =-1, q =3 & ~A (-1,-1,-1) B (9,3,1) aligned | array ccc 1 & 0 & 1 -1 & -1 &

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