A) \[\frac{\sqrt{65}}{2}\]
B) \[\frac{\sqrt{91}}{4}\]
C) \[2\sqrt{13}\]
D) \[\frac{\sqrt{91}}{2}\]
Correct Answer: D
Solution :
R lies on the plane. \[DQ=\frac{|1-12-2|}{\sqrt{9+1+16}}=\frac{13}{\sqrt{26}}=\sqrt{\frac{13}{2}}\]\[\Rightarrow PQ=\sqrt{26}\] Now,\[RQ=\sqrt{9+1}=\sqrt{10}\] \[\Rightarrow RD=\sqrt{10-\frac{13}{2}}=\sqrt{\frac{7}{2}}\] Hence,\[ar(\Delta PQR)=\frac{1}{2}\times \sqrt{26}\times \sqrt{\frac{7}{2}}=\sqrt{\frac{91}{2}}.\]You need to login to perform this action.
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