Correct Answer: Option D

Explanation

r = (10 N, 200º) and n = (16 N, 020º)

In rectangular form:

r = 10cos 200ºi + 10sin 200ºj = -9.397i - 3.420j

n = 16cos 20ºi + 16sin 20ºj = 15.035i + 5.472j

3r = -28.191i - 10.260j

2n = 30.070i + 10.945j

3r - 2n = (-28.191i - 10.260j) - (30.070i + 10.945j)

3r - 2n = -58.261i - 21.205j

|3r - 2n| = √((-58.261)\(^2\) + (-21.205)\(^2\)) = 62 N

\(tan θ =\frac{-21.205}{-58.261} = 0.3640\)

\(θ = tan^{-1} (0.3640) = 20^o\)

∴ (62 N , 020º)

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