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KCET2019MathematicsThree Dimensional Geometry

Acute angle between the line ( x-5 2 = y+1 -1 = z+4 1 ) and the plane ( 3 x-4 y-z+5=0 ) is

Options

  1. A( ⁻¹ ( 9 364 ) )
  2. B( ⁻¹ ( 9 2 13 ) )
  3. C( ⁻¹ ( 9 364 ) )
  4. D( ⁻¹ ( 5 2 13 ) )

Correct answer

D. ( ⁻¹ ( 5 2 13 ) )

Step-by-step solution

( L: (x-5) 2 = (y+1) -1 = (z+4) 1 ) Dr's of line: ( 2,-1,1 ) P: ( 3 x-4 y-z+5=0 ) Dr's of normal to plane: ( -3,4,1 ) ( = | -6-4+1 4+1+1 9+16+1 |= | -9 156 | ) [ array l = 9 156 = ⁻¹ ( 9 156 ) = ⁻¹ ( 9 2 39 ) = ⁻¹ ( 5 2 13 ) array ]

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