A) \[5x+y+12z-23=0\]
B) \[5x+6y+\text{ }2z-23=0\]
C) \[x+\text{ }6y+\text{ }2z-13=0\]
D) \[x+y+2-13=0\]
E) \[5x+y+z-23=0\]
Correct Answer: B
Solution :
Equation of plane through (1, 2, 3) is \[a(x-1)+b(y-2)+c(z-3)=0\] ...(i) It passes through (-1, 4, 2) and (3, 1, 1) \[-2a+2b-c=0\] ...(ii) and \[2a-b-2c=0\] ...(iii) From Eqs. (ii) and (iii) \[\frac{a}{-5}=\frac{b}{-6}=\frac{c}{-2}\] \[\therefore \]Equation of plane is \[-5x-6y-2z+5+12+6=0\] \[\Rightarrow \] \[5x+6y+2z-23=0\]
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