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JEE Main2014MathematicsThree Dimensional GeometryActual

The plane containing the line x -1 1 = y -2 2 = z -3 3 and parallel to the line x 1 = y 1 = z 4 passes through the point:

Options

  1. A(1,-2,5)
  2. B(1,0,5)
  3. C(0,3,-5)
  4. D(-1,-3,0)

Correct answer

B. (1,0,5)

Step-by-step solution

Equation of the plane containing the line x-1 1 = y-2 2 = z-3 3 is a(x-1)+b(y-2)+c(z-3)=0 where a .1+b .2+c .3=0 i.e., a+2 b+3 c=0 (ii) Since the plane (i) parallel to the line array ll & x 1 = y 1 = z 4 & a .1+b .1+c .4=0 i.e., & a + b +4 c =0 array (iii) From (ii) and (iii), gathered a 8-3 = b 3-4 = c 1-2 =k (let) a=5 k, b=-k, c=-k gathered On putting the value of a, b and c in equation (i), aligned &5(x-1)-(y-2)-(z-3)=0 & 5 x-y-z=0 aligned when x=1, y=0 and z=5 ; then L.H.S. of equation (iv) =5 x-y-2 aligned &=5

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