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BITSAT2012MathematicsThree Dimensional GeometryActual

Find the coordinates of the point where the line joining the points (2,-3,1) and (3,-4,-5) cuts the plane 2 x+y+z=7

Options

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

Correct answer

B. (1,-2,7)

Step-by-step solution

The direction ratios of the line are 3-2,-4-(-3),-5-1 i.e. 1,-1,-6 Hence equation of the line joining the given points is x-2 1 = y+3 -1 = z-1 -6 =r( say ) Coordinates of any point on this line are (r+2,-r-3,-6 r+1) If this point lies on the given plane 2 x+y+z=7 then 2(r+2)+(-r-3)+(-6 r+1)=7 r=-1 Coordinates of any point on this line are (-1+2,-(-1)-3,-6(-1)+1) i.e. (1,-2,7)

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