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Two forces F1=(7i+8j)N and F2=(3i+4j)N...

Two forces F1=(7i+8j)N and F2=(3i+4j)N act on a particle. Find the magnitude and direction of F1F2

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 is B

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°)