A) \[\pm 3\]
B) \[\pm 6\]
C) ?3, 9
D) \[3,\,-9\]
Correct Answer: D
Solution :
Distance of the point (1,1,1) from origin \[=\sqrt{{{(1)}^{2}}+{{(1)}^{2}}+{{(1)}^{2}}}=\sqrt{3}\] Distance of the point (1,1,1) from \[x+y+z+k=0\] is, \[\pm \frac{(1)+(1)+(1)+k}{\sqrt{{{(1)}^{2}}+{{(1)}^{2}}+{{(1)}^{2}}}}=\pm \frac{k+3}{\sqrt{3}}\] According to question, \[\sqrt{3}=\pm \frac{1}{2}\left( \frac{k+3}{\sqrt{3}} \right)\] Þ \[6=\pm (k+3)\]Þ\[k=3,-9\]. 3, 9
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