A) \[x+y+4z=7\]
B) \[x+4z=7\]
C) \[y-4z=7\]
D) \[y+4z=-7\]
E) \[y+4z=7\]
Correct Answer: E
Solution :
We know that the equation of a plane parallel to\[x-\]axis is \[by+cz+d=0\] Since, it passes through the points (2 3 1) and\[(4,-5,3)\]. \[\therefore \] \[3b+c+d=0\] ?(i) and \[-5b+3c+d=0\] ...(ii) On solving Eqs. (i) and (ii), we get \[\frac{b}{1-3}=\frac{c}{-8}=\frac{d}{14}\] \[\Rightarrow \] \[\frac{b}{-2}=\frac{c}{-8}=\frac{d}{14}\] \[\therefore \]Equation of plane is \[-2y-8z+14=0\] \[\Rightarrow \]\[y+4z=7\]
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