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JEE Advanced2022MathematicsThree Dimensional GeometryActual

Let P 1 and P 2 be two planes given by P 1 : 10 x + 15 y + 12 z - 60 = 0 , P 2 : - 2 x + 5 y + 4 z - 20 = 0 . Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on P 1 and P 2 ?

Options

  1. Ax - 1 0 = y - 1 0 = z - 1 5
  2. Bx - 6 - 5 = y 2 = z 3
  3. Cx - 2 = y - 4 5 = z 4
  4. Dx 1 = y - 4 - 2 = z 3

Correct answer

A. x - 1 0 = y - 1 0 = z - 1 5

Step-by-step solution

Given, P 1 and P 2 be two planes given by P 1 : 10 x + 15 y + 12 z - 60 = 0 , P 2 : - 2 x + 5 y + 4 z - 20 = 0 . Now finding line of intersection of both the planes, Let z = λ then we have equations, 10 x + 15 y = 60 - 12 λ   . . . 1 - 2 x + 5 y = 20 - 4 λ   . . . . . 2 Now on solving equation 1   &   2 we get, x 0 = y - 4 - 4 = z 5 Replacing  λ   with  z Now any skew line with the line of intersection of given plane can be edge of tetrahedron, Or any line

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