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KCET2018MathematicsThree Dimensional Geometry

The value of ( k ) such that the line ( x-4 1 = y-2 1 = z-k 2 ) lies on the plane ( 2 x-4 y+z=7 ) is

Options

  1. A( -7 )
  2. B( 4 )
  3. C( -4 )
  4. D( 7 )

Correct answer

D. ( 7 )

Step-by-step solution

Given line, [ x-4 1 = y-2 1 = z-k 2 (1) ] So, point ( (4,2, k ) ) lies on the line Given plane, ( 2 x-4 y+z=7 (2) ) Point ( (4,2, k ) ) satisfies the plane. So, [ array l 2(4)-4(2)+k=7 8-8+k=7 k=7 array ]

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