A) \[9\]
B) \[3\]
C) \[1/9\]
D) \[1/3\]
Correct Answer: A
Solution :
Given plane cuts the coordinate axes at\[A(a,\,\,0,\,\,0)\],\[B(0,\,\,b,\,\,0)\] and\[C(0,\,\,0,\,\,c)\]. It is at a unit distance from the origin. \[\therefore \] \[\frac{1}{\sqrt{\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}+\frac{1}{{{c}^{2}}}}}=1\] \[\Rightarrow \] \[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}+\frac{1}{{{c}^{2}}}=1\] ? (i) Since, \[(x,\,\,y,\,\,z)\] is the centroid of\[\Delta ABC\]. \[\therefore \] \[x=\frac{a}{3},\,\,y\frac{b}{3}\,\,and\,\,z=\frac{c}{3}\] \[\Rightarrow \] \[a=3x,\,\,b=3y\,\,c=3z\] On substituting the values of a, b and c in Eq. (i), we get \[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}+\frac{1}{{{z}^{2}}}=9\] \[\therefore \] \[k=9\]You need to login to perform this action.
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