A) \[x+2y+3z=9\]
B) \[2x-3y-6z=18\]
C) \[2x+3y+6z=18\]
D) \[2x+y+6z=18\]
E) \[2x+3y+6z=9\]
Correct Answer: C
Solution :
Coordinates of A, B and C are (a, 0, 0), (0, b, 0) and (0, 0, c) respectively Since, centroid of\[\Delta ABC\]is (3, 2, 1). \[\therefore \] \[\frac{a+0+0}{3}=3\] \[\Rightarrow \] \[a=9\] And \[\frac{0+b+0}{3}=2\] \[\Rightarrow \] \[b=6\] And \[\frac{0+0+c}{3}=1\] \[\Rightarrow \] \[c=3\] \[\therefore \]Equation of required plane is \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\] \[\Rightarrow \] \[\frac{x}{9}+\frac{y}{6}+\frac{z}{3}=1\] \[\Rightarrow \] \[2x+3y+6z=18\]
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