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BITSAT2013MathematicsThree Dimensional GeometryActual

Find the angle between the two planes 2 x + y -2 z =5 and 3 x-6 y-2 z=7

Options

  1. A⁻¹(4 / 21)
  2. B⁻¹(2 / 21)
  3. C⁻¹(1 / 21)
  4. D⁻¹(5 / 21)

Correct answer

A. ⁻¹(4 / 21)

Step-by-step solution

The angle between two planes is the angle between their normals. From the equation of the planes, the normal vectors are N ₁=2 i + j -2 k and N ₂=3 i -6 j -2 k Therefore, = | N ₁ N ₂ | N ₁ | | N ₂ | | = | (2 i + j -2 k ) (3 i -6 j -2 k ) 4+1+4 9+36+4 |= ( 4 21 ) Hence, = ⁻¹ ( 4 21 )

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