A) 1 : 3
B) 3 : 1
C) 2 : 8
D) 3 : 2
Correct Answer: B
Solution :
[b]\[\frac{\text{Area}\,\text{of}\,\Delta ABC}{\text{Area}\,\text{of}\,\Delta OAC}\]\[=\frac{\frac{1}{2}[|OA\times OB|+|OB\times OC|+|OC\times OA|}{\frac{1}{2}|OA\times OC|}\]\[=\frac{|OA\times OB|+OB\times OC|}{|OA\times OC|}+1\] |
Given, \[OA+2OB+3OC=0\] |
\[2OB\times OA+3OC\times OA=0\] |
\[\Rightarrow \]\[\frac{|OB\times OA|}{3}=\frac{|OC\times OA|}{2}=\lambda \] |
\[OB\times OA+3OB\times OC=0\] |
\[\Rightarrow \]\[\frac{|OB\times OA|}{3}=\frac{|OB\times OC|}{1}=\lambda \] |
\[\frac{\text{Area}\,\text{of}\,\Delta ABC}{\text{Area}\,\text{of}\,\Delta AOC}=\frac{3\lambda +\lambda }{2\lambda }+1=3:1\] |
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