In a two dimensional motion of a particle, the particle moves from point $A$, position vector ${\overrightarrow{r}}_{1}$. If the magnitudes of these vectors are respectively, $r_{1}$=3 and $r_{2} = 4$ and the angles they make with the $x$-axis are $ heta_{1} = 75{^\circ}$ and 15${^\circ}$, respectively, then find the magnitude of the displacement vector [image:4_image2.emf]

Question

In a two dimensional motion of a particle, the particle moves from point $A$, position vector ${\overrightarrow{r}}_{1}$. If the magnitudes of these vectors are respectively, $r_{1}$=3 and $r_{2} = 4$ and the angles they make with the $x$-axis are $	heta_{1} = 75{^\circ}$ and 15${^\circ}$, respectively, then find the magnitude of the displacement vector [image:4_image2.emf]

Dr. Abubacker · Accepted Answer

(c) Displacement $= AB$
angle between $\overrightarrow{r_{1}}$ and $\overrightarrow{r_{2}}$
$	heta = 75{^\circ} - 15{^\circ} = 60{^\circ}$
From figure
$AB^{2} = r_{1}^{2} + r_{2}^{2} - 2r_{1}r_{2}cos	heta$
$= 3^{2} + 4^{2} - 2 	imes 3 	imes 4$ cos$60{^\circ}$
$= 13$
$AB = \sqrt{13}$

Explanation

Reviewed by Dr. Abubacker

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