InterviewSolution
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InterviewSolution
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Statement 1: The plane `5x+2z-8=0` contains the line `2x-y+z-3=0` and `3x+y+z=5`, and is perpendicular to `2x-y-5z-3=0`. Statement 2: The plane `3x+y+z=5`, meets the line `x-1=y+1=z-1` at the point (1,1,1)A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True. |
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Answer» Correct Answer - C The equation of the family of planes containing the line `2x-y+z-3=0,3x+y+z=5` is `2x-y+z-3+lamda(3x+y+z-5)=0` For `lamda=1` this reduces to `5x+2z-8=0` So the plane `5x+2z-8=0` contains the given line. Also `2xx5-1xx0-5xx2=0` So, the plane `5x+2z-8=0` is perpendicular to `2x-y-5z-3=0` Hence, statement -1 is true. The coordinate of any point on line `(x-1)/1=(y+1)/1=(z-1)/1` are `(r+1,r-1,r+1)`. If this point lies on the plane `3x+y+z=5`. Then, `3r+3r-1+r+1=5impliesr=2/5` Thus, the line meets the plane at `(7/5,-3/5,7/5)` So, Statemnet -2 is not true. |
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