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JEE Main2018MathematicsThree Dimensional GeometryActual

The length of the projection of the line segment joining the points ( 5 , - 1 , 4 ) and ( 4 , - 1 , 3 ) on the plane, x + y + z = 7 is

Options

  1. A2 3
  2. B2 3
  3. C2 3
  4. D1 3

Correct answer

A. 2 3

Step-by-step solution

DR's of A A ' ( 1 ,   1 ,   1 ) , as this will be normal to the plane. DR's of A B is ( 1 ,   0 ,   1 ) ⇒ cos ⁡ θ = 1 × 1 + 1 × 0 + 1 × 1 1 2 + 1 2 + 1 2 1 2 + 0 2 + 1 2 = 2 6 = 2 3   ,   also A B = 2 Projection A 1 B 1 = 2 . sin ⁡ θ = 2 . 1 - 2 3 = 2 3  

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