A) \[\sqrt{66}\]
B) \[\sqrt{71}\]
C) \[\sqrt{73}\]
D) \[\sqrt{76}\]
Correct Answer: A
Solution :
Equation of plane passing through \[(-1,\,3,\,0)\] is \[A(x+1)+B(y-3)+C(z-0)=0\] ......(i) Also, plane (i) is passing through the points \[(2,\,2,\,1)\] and (1, 1, 3). So, \[3A-B+C=0\] .....(ii) \[2A-2B+3C=0\] .....(iii) Solving (ii) and (iii), \[\frac{A}{-3+2}=\frac{B}{2-9}=\frac{C}{-6+2}\] \ \[A:B:C=-1:-7:-4\] or \[A:B:C=1:7:4\] From (i), \[1(x+1)+7(y-3)+4(z)=0\] or \[x+7y+4z-20=0\] \[\therefore \]Distance from the plane to the point (5, 7, 8) is, \[\frac{1\times 5+7\times 7+4\times 8-20}{\sqrt{{{1}^{2}}+{{7}^{2}}+{{4}^{2}}}}=\frac{5+49+32-20}{\sqrt{66}}=\frac{66}{\sqrt{66}}=\sqrt{66}\].
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