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MHT CET202020 Oct 2020Morning ShiftMathematicsThree Dimensional GeometryActual

If the lines x-1 2 = y +1 3 = z -1 4 and x-3 1 = y - k 2 = z 1 interect, then the value of the k is

Options

  1. A. -2 9
  2. B2 9 2
  3. C3. 3 2
  4. D4 -3 2

Correct answer

B. 2 9 2

Step-by-step solution

Let ( x ₁, y ₁, z ₁ ) (1,-1,1) and ( x ₂, y ₂, z ₂ ) (3, k , 0) Let ( a ₁, ~b ₁, c ₁ ) (2,3,4) and let ( a ₂, ~b ₂, c ₂ ) (1,2,1) Since, the lines intersect | array ccc x₂-x₁ & y₂-y₁ & z₂-z₁ a₁ & b₁ & c₁ a₂ & b₂ & c₂ array |=0 | array ccc 2 & k+1 & -1 2 & 3 & 4 1 & 2 & 1 array |=02(3-8)-(k+1)(2-4)-1(4-3)=0-10+2 k+2-1=0 k= 9 2

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