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BITSAT2014MathematicsThree Dimensional GeometryActual

Find the angle between the line x+1 2 = y 3 = z-3 6 and the plane 10 x +2 y -11 z =3

Options

  1. A⁻¹ ( 8 21 )
  2. B⁻¹ ( 5 21 )
  3. C⁻¹ ( 7 21 )
  4. D⁻¹ ( 1 21 )

Correct answer

A. ⁻¹ ( 8 21 )

Step-by-step solution

Let be the angle between the line and the normal to the plane. Converting the given equations into vector form, we have r =(- i +3 k )+ (2 i +3 j +6 k ) and r (10 i +2 j -11 k )=3 Here, b =2 i +3 j +6 k and n =10 i +2 j -11 k array l = | (2 i +3 j +6 k ) (10 i +2 j -11 k ) 2²+3²+6² 10²+2²+11² | = | -40 7 15 |= | -8 21 |= 8 21 or = ⁻¹ ( 8 21 ) array

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