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MHT CET202311 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The lines x-1 3 = y+1 2 = z-1 5 and x+2 4 = y-1 3 = z+1 2

Options

  1. Aintersect each other and point of intersection is (2,1,3)
  2. Bintersect each other and point of intersection is (3,2,4)
  3. Cintersect each other and point of intersection is (-2,3,3)
  4. Ddo not intersect.

Correct answer

D. do not intersect.

Step-by-step solution

The given lines are x-1 3 = y+1 2 = z-1 5 and x+2 4 = y-1 3 = z+1 2 aligned & Here, & (x₁, y₁, z ₁ ) (1,-1,1) & (x₂, y₂, z ₂ ) (-2,1,-1) & ( a ₁, ~b ₁, c ₁ ) (3,2,5) & Consider | array ccc x₂-x₁ & y₂-y₁ & z ₂- z ₁ a ₁ & ~b ₁ & c ₁ a ₂ & ~b ₂ & c ₂ array | & = | array ccc -3 & 2 & -2 3 & 2 & 5 4 & 3 & 2 array | & =-3(-11)-2(-14)-2(1) & =33+28-2 & =59 0 aligned The lines are not intersecting.

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