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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Let L be a straight line passing through origin. Suppose that all the points on L are at constant distance from the two planes P₁: x+3 y-z+1=0 and P₂: 3 x-y+z-1=0 then which of the following points lie(s) on the line L :

Options

  1. A(1,-2,-5)
  2. B(1,-2,5)
  3. C(-1,-2,5)
  4. D(-1,2,5)

Correct answer

D. (-1,2,5)

Step-by-step solution

Clearly L should be parallel to both the planes P₁ and P₂ . L is perpendicular to both normals n ₁ = i +3 j - k and n ₂ =3 i - j + k n ₁ n ₂ = | array ccc i & j & k 1 & 3 & -1 3 & -1 & 1 array |=2 i -4 j -10 k Dr's of L=(1,-2,-5) Equation of L is x 1 = y -2 = z -5 Point (1,-2,-5) and (-1,2,5) lie on L .

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