A) \[\sqrt{{{({{F}_{3}}-{{F}_{1}})}^{2}}-F_{2}^{2}}\]
B) \[{{F}_{3}}+{{F}_{1}}-{{F}_{2}}\]
C) \[{{F}_{3}}-{{F}_{1}}+{{F}_{2}}\]
D) \[\sqrt{{{({{F}_{3}}-{{F}_{1}})}^{2}}+F_{2}^{2}}\]
Correct Answer: D
Solution :
[d] If \[{{F}_{4}}\] is the force on segment QP, then \[{{\vec{F}}_{1}}+{{\vec{F}}_{2}}+{{\vec{F}}_{3}}+{{\vec{F}}_{4}}=0\] and \[{{\overset{_{\to }}{\mathop{F}}\,}_{4}}=-({{\overset{\to }{\mathop{F}}\,}_{1}}+{{\overset{\to }{\mathop{F}}\,}_{2}}+{{\overset{\to }{\mathop{F}}\,}_{3}})\] or \[{{F}_{4}}=\sqrt{{{({{F}_{3}}-{{F}_{1}})}^{2}}+F_{2}^{2}.}\]
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