Question

In a two dimensional motion of particle, the particle moves from point Α, position vector ${\overrightarrow{r}}_1$ to point B, position vector ${\overrightarrow{r}}_2$. If the magnitudes of these vectors are, respectively $r_1=3and{r}_2=4$, and the angles they make with the x- axis are ${\theta }_1={75}^{0}and{\theta }_2={15}^0,$ and respectively, then find the magnitude of the displacement vector.

• A. 15
• B. $\sqrt{13}$
• C. 17
• D. $\sqrt{15}$

Answer 1

The correct option is B

$\sqrt{13}$

$Anglebetween\overline{r_1}and\overline{r_2}:\theta ={70}^0-{15}^0={60}^{0}R=\sqrt{r_1^2+r_2^2+2r_1{r}_{2}cos(180-{60}^0)}=\sqrt{3^2+4^2-2\times 3\times 4cos{60}^0}=\sqrt{13}\Rightarrow AB=\sqrt{13}$