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COMEDK2023MathematicsThree Dimensional Geometry

The place x-2 y+z=0 is parallel to the line

Options

  1. Ax-3 4 = y-4 5 = z-3 6
  2. Bx-2 1 = y-2 -2 = z-3 1
  3. Cx-2 2 = y-3 3 = z-4 4
  4. Dx-4 3 = y-5 4 = z-6 3

Correct answer

A. x-3 4 = y-4 5 = z-3 6

Step-by-step solution

Consider the equation of line given in option (a). The DR's of this line or (4,5,6) . We know that if the line x-x₀ a₁ = y-y₀ b₁ = z-z₀ c₁ is parallel to the plane a₂ x+b₂ y+c₂ z+d=0 , then a₁ a₂+b₁ b₂+c₁ c₂=0 , that is the normal to the plane is perpendicular to the line. Here, the vector i -2 j + k is normal to the plane x-2 y+z=0 and 4(1)+5(-2)+6(1)=4-10+6=10-10=0 So, option (a) is correct.

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