A) \[(-6,0,0)\]
B) \[(5,0,0)\]
C) \[(-5,0,0)\]
D) \[(6,0,0)\]
Correct Answer: D
Solution :
Let the point on x-axis is \[A(x,0,0)\] we have, \[B=(1,2,3)\] and \[C=(3,5,-2).\] Now, \[|AB|=|AC|\] \[\Rightarrow \]\[\sqrt{{{(x-1)}^{2}}+{{(0-2)}^{2}}+{{(0-3)}^{3}}}\] \[=\sqrt{{{(x-3)}^{2}}+{{(0-5)}^{2}}+{{(0+2)}^{3}}}\] \[\Rightarrow \] \[{{x}^{3}}+1-2x+4+9={{x}^{2}}+9-6x+25+4\] \[\Rightarrow \] \[4x=24\] \[\Rightarrow \] \[x=6\] \[\therefore \] Required point is \[(6,0,0)\].
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