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Question

The lines fraction numerator x minus 3 over denominator 2 end fraction equals fraction numerator y minus 2 over denominator 3 end fraction equals fraction numerator z minus 1 over denominator lambda end fraction and  lie in a same plane. Based on this information answer the following. Equation of the plane containing both lines

  1. x+5y-3z=10
  2. x+6y+5z=20
  3. x+6y-5z=10
  4. None

hintHint:

Product of the coordinates of the points should be zero and then verify the lines.

The correct answer is: x+6y-5z=10


    Given That:
    The lines fraction numerator x minus 3 over denominator 2 end fraction equals fraction numerator y minus 2 over denominator 3 end fraction equals fraction numerator z minus 1 over denominator lambda end fraction and  lie in a same plane. Based on this information answer the following. Equation of the plane containing both lines
    >>> The directional ratios of the given lines are: (3,2,1) and (1,-1,1-lambda).
    >>> Therefore, both remains in the same plane. Then,
    3 -2+1-lambda =0
    lambda = 2.
    >>> The value of lambda is 2.

    >>> the equation of the line should satisfy the above points (3,2,1) and (1,-1,1-lambda) becomes: 
                         x+6y-5z=10.
    >>> Therefore, the equation of the line becomes x+6y-5z=10.

     Therefore, the equation of the line becomes x+6y-5z=10.

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