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MHT CET202411 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

If for some R , the lines L ₁: x+1 2 = y-2 -1 = z-1 1 and L ₂: x+2 = y+1 5- = z+1 1 are coplanar, then the line L ₂ passes through the point

Options

  1. A(10,2,2)
  2. B(2,-10,-2)
  3. C(10,-2,-2)
  4. D(-2,10,2)

Correct answer

B. (2,-10,-2)

Step-by-step solution

Here x₁, y₁, z ₁=-1,2,1 and x₂, y₂, z ₂=-2,-1,-1a₁, b₁, c₁=2,-1,1 and a₂, b₂, c₂= , 5- , 1 Since the given lines are coplanar, we get aligned & | array ccc x₂-x₁ & y₂-y₁ & z₂-z₁ a₁ & b₁ & c₁ a₂ & b₂ & c₂ array |=0 & | array ccc -2+1 & -1-2 & -1-1 2 & -1 & 1 & 5- & 1 array |=0 aligned aligned & (-1)(-1-5+ )-(-3)(2- ) & +(-2)(10-2 + )=0 & 6- +6-3 -20+2 =0 & =-4 & L₂: x+2 -4 = y+1 9 = z+1 1 aligned Only option (B) satisfies the equation of line L ₂ .

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