A) \[(-\,3,0,-1)\]
B) \[(3,3,-1)\]
C) \[(3,2,1)\]
D) \[(-\,3,1,1)\]
Correct Answer: C
Solution :
Plane through the intersection of the given planes is of the form |
\[(x+y+z\,-\,1)\,+\,\lambda \,(2x+3y-z+4)\,=\,0\] |
\[(2\lambda +1)x\,+\,(3\lambda +1)y+\,(1-\lambda )z+\,(4\lambda -1)\,=\,0,\lambda \,\in \,R\] |
This is parallel to y-axis \[\Rightarrow \]\[3\lambda \,+\,1\,=\,0\] |
\[\therefore \] \[\lambda \,=\,-\,\text{1/3}\] |
\[\therefore \]The equation.of the plane is \[x\,+\,4z-\,7\,=\,0\] |
It is passing through (3, 2, 1). |
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