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  4. The angle between two vectors of magnitudes 12 N and 3N on a body is 60° the resultant w .r.t. 12 N force is about

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Q. The angle between two vectors of magnitudes 12 N and 3N on a body is 60$^\circ$ the resultant w .r.t. 12 N force is about

Motion in a Plane

Solution:

Using, tan $\theta = \frac{F_2 \, sin \, \theta}{F_1 + F_2 \, cos \, \theta}$ we get,
$tan \, \alpha = \frac{3sin \, 60^\circ}{12 + 3 cos \, 60^\circ} $
$\frac{3\times\sqrt{3/2}}{12+3\times1/2}=\frac{3\sqrt{3}}{27}$
=$\frac{5.1962}{2}=0.19245$
$\therefore \alpha=10.9^\circ$