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.
((4sqrt{2} N, 000°)) -
B.
((4sqrt{2} N, 045°)) -
C.
((4sqrt{2} N, 090°)) -
D.
((4sqrt{2} N, 180°))
Correct Answer: Option 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} = 4sqrt{2})
(tan theta = frac{y}{x} = frac{4}{4} = 1)
(theta = tan^{-1} 1 = 045°)
= ((4sqrt{2} N, 045°))