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For the following two (02) items: A plane P is parallel to the line having direction ratios 1, 3, 2 and contains the line of intersection of the planes 6x + 4y - 5z = 2 and x - 2y + 3z = 0 . Which of the following are the direction ratios of the line of intersection of the given planes?

Options

  1. A2, 23, 16
  2. B2, -23, -16
  3. C2, 3, 2
  4. D-1, 3, -2

Correct answer

B. 2, -23, -16

Step-by-step solution

The normal vectors of the given planes are n ₁ = 6, 4, -5 and n ₂ = 1, -2, 3 . The direction vector d of the line of intersection of the planes is given by the cross product of their normal vectors: d = n ₁ n ₂ = vmatrix i & j & k 6 & 4 & -5 1 & -2 & 3 vmatrix d = i (12 - 10) - j (18 + 5) + k (-12 - 4) d = 2 i - 23 j - 16 k The direction ratios of the line of intersection are 2, -23, -16 . Answer: 2, -23, -16

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