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Manipal MET2014MathematicsThree Dimensional Geometry

The line joining the points (1,1,2) and (3,-2,1) meets the plane 3 x+2 y+z=6 at the point

Options

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

Correct answer

B. (3,-2,1)

Step-by-step solution

The straight line joining the points (1,1,2) and (3,-2,1) is x-1 2 = y-1 -3 = z-2 -1 =r (say) point is (2 r+1,1-3 r, 2-r) which lies on 3 x+2 y+z=6 3(2 r+1)+2(1-3 r)+2-r=6 r=1 So, required point is (3,-2,1) .

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