A) \[5\text{ }N\]making an angle \[\theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)\] with the negative y-axis
B) \[5\text{ }N\]making an angle \[\theta ={{\tan }^{-1}}\left( \frac{4}{3} \right)\] with the negative y-axis
C) \[7\text{ }N\]making an angle \[\theta ={{\tan }^{-1}}\left( \frac{3}{4} \right)\] with the negative y-axis
D) \[7\text{ }N\] making an angle \[\theta ={{\tan }^{-1}}\left( \frac{4}{3} \right)\] with the negative y-axis
Correct Answer: A
Solution :
Resultant, \[R=\sqrt{{{x}^{2}}+{{y}^{2}}}\] \[R=\sqrt{{{3}^{2}}+{{4}^{2}}}\] \[R=\sqrt{25}=5N\] and \[\cos \theta =\frac{x}{R}=\frac{3}{5}\] \[sin\theta =\frac{y}{R}=\frac{4}{5}\] then \[\tan \theta =\frac{y}{x}=\frac{4}{3}\] \[\theta ={{\tan }^{-1}}\left( \frac{4}{3} \right)\] with negative y-axis.
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