A) \[\sqrt{2}\]
B) 2
C) \[\sqrt{3}\]
D) 1
Correct Answer: C
Solution :
Point P is (2,-1,2) Let this line meet at Q (h, k, w) Direction ratio of this line is\[(h-2,k+1,w-2)\] Since, \[d{{c}_{s}}\]are equal &\[d{{r}_{s}}\] are also equal, So,\[h-2=k+1+w-2\]\[\Rightarrow \]\[k=h-3\] andw= h This line meets the plane \[2x+y+z=9\]at Q, so, \[2h+k+w=9\]or\[2h+h-3+h=9\] \[\Rightarrow \]\[4h-3=9\]\[\Rightarrow \]\[h=3\]and\[k=0\]and\[w=3\] Distance \[PQ=\sqrt{{{\left( 3-2 \right)}^{2}}+{{\left( 0-(-1) \right)}^{2}}+{{\left( 3-2 \right)}^{2}}}\]\[=\sqrt{{{1}^{2}}+{{1}^{2}}+{{1}^{2}}}=\sqrt{3}\]
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