Two forces \(F_{1} = (7i + 8j)N\) and \(F_{2} = (3i + 4j)N\) act on a particle. Find the magnitude and direction of \(F_{1} - F_{2}\).
A. \((4\sqrt{2} N, 000°)\)
B. \((4\sqrt{2} N, 045°)\)
C. \((4\sqrt{2} N, 090°)\)
D. \((4\sqrt{2} N, 180°)\)
Correct Answer: B
Explanation
\(F_{1} = (7i + 8j)N ; F_{2} = (3i + 4j)N\)
\(|F_{1} - F_{2}| = |(7i + 8j) - (3i + 4j)| = |4i + 4j|\)
\(|4i + 4j| = \sqrt{4^{2} + 4^{2}} = \sqrt{32} = 4\sqrt{2}\)
\(\tan \theta = \frac{y}{x} = \frac{4}{4} = 1\)
\(\theta = \tan^{-1} 1 = 045°\)
= \((4\sqrt{2} N, 045°)\)
