A) \[-\frac{17}{146}\]
B) \[\frac{17}{146}\]
C) \[\left| \begin{matrix} a & {{a}^{2}} & 1+{{a}^{3}} \\ b & {{b}^{3}} & 1+{{b}^{3}} \\ c & {{c}^{3}} & 1+{{c}^{3}} \\ \end{matrix} \right|=0\]
D) \[(1,a,{{a}^{2}})\]
Correct Answer: A
Solution :
\[2\overset{\to }{\mathop{OA}}\,+3\overset{\to }{\mathop{OB}}\,=2(\overset{\to }{\mathop{OC}}\,+\overset{\to }{\mathop{CA}}\,)+3(\overset{\to }{\mathop{OC}}\,+\overset{\to }{\mathop{CB}}\,)\] \[=5\overset{\to }{\mathop{OC}}\,+2\overset{\to }{\mathop{CA}}\,+3\overset{\to }{\mathop{CB}}\,\] \[=5\overset{\to }{\mathop{OC}}\,\] \[[\because 2\overset{\to }{\mathop{CA}}\,=-3\overset{\to }{\mathop{CB]}}\,\]
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