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KCET2014MathematicsDeterminants

The line ( x-2 3 = y-3 4 = z-4 5 ) is parallel to the plane

Options

  1. A( 3 x+4 y+5 z=7 )
  2. B( x+y+z=2 )
  3. C( 2 x+3 y+4 z=0 )
  4. D( 2 x+y-2 z=0 )

Correct answer

D. ( 2 x+y-2 z=0 )

Step-by-step solution

Given that, x-2 3 = y-3 4 = z-4 5 (1) So, direction ratio's of line are 3,4,5 Since, line and plane are parallel. So, normal to plane and line are perpendicular Now, a₁ a₂+b₁ b₂+c₁ c₂=0 for plane 2 x+y-2 z=0 Now, 3(2)+4(1)-2(5)=0 Hence, required equation is 2 x+y-2 z=0

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