A) \[{{F}_{1}}=3N,\,\,{{F}_{2}}=5N,\,\,{{F}_{3}}=9N\]
B) \[{{F}_{1}}=3N,\,\,{{F}_{2}}=5N,\,\,{{F}_{3}}=1N\]
C) \[{{F}_{1}}=3N,\,{{F}_{2}}=5N,\,{{F}_{3}}=15N\]
D) \[{{F}_{1}}=3N,\,\,{{F}_{2}}=5N,\,\,{{F}_{3}}=6N\]
Correct Answer: D
Solution :
Range of resultant of \[{{F}_{1}}\] and \[{{F}_{2}}\] varies between \[\left( 3+5 \right)\text{ }=\text{ }8N\] and \[(5-3)=2N\]. It means for some value of angle \[(\theta )\], resultant 6 can be obtained. So, the resultant of 3N, 5N and 6N may be zero and the forces may be in equilibrium.
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