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BITSAT2011MathematicsThree Dimensional GeometryActual

Gives the line (L: x-1 3 = y+1 2 = z-3 -1 ) and the plane ( : x-2 y-z=0 ). Of the following assertions, the only one that is always true is

Options

  1. AL is ( ) to ( )
  2. BL lies in ( )
  3. CL is not parallel to ( )
  4. DNone of these

Correct answer

B. L lies in ( )

Step-by-step solution

Since (3(1)+2(-2)+(-1)(-1)=3-4+1=0 ) ( ) Given line is ( ) to the normal to the plane i.e., given line is parallel to the given plane. Also, ((1,-1,3) ) lies on the plane (x-2 y-z=0 ) if (1-2(-1)-3=0 ) i.e., (1+2-3=0 ) which is true ( ) L lies in plane ( ).

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