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AP EAMCET202123 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual

The angle between the planes 2 x-y+z=6 and x+y+2 z=3 is

Options

  1. A3
  2. B⁻¹ ( 1 6 )
  3. C4
  4. D6

Correct answer

A. 3

Step-by-step solution

Given, planes are 2 x-y+z=6 and x+y+2 z=3 General equation of plane is a x+b y+c z=d Normal vector of plane is a i +b j +c k . For plane 2 x-y+z=6 n ₁=2 i - j + k For plane x+y+2 z=3 n ₂= i + j +2 k Angle between n₁ and n₂ is given as, aligned = | n ₁ n ₂ | | n ₁ | | n ₂ | & = (2-1+2) 4+1+1 1+1+4 & = 3 6 = 1 2 & = / 3 aligned Angle between given planes is 3 .

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