If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude $\mathrm{R}$ are inclined at an angle $\theta$, then
$|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}|=\sqrt{2} \mathrm{R} \sin \left(\frac{\theta}{2}\right)$
$|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=2 \mathrm{R} \sin \left(\frac{\theta}{2}\right)$
$|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=2 \mathrm{R} \cos \left(\frac{\theta}{2}\right)$
$|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}|=2 R \cos \left(\frac{\theta}{2}\right)$
If $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$ then magnitude and direction of $\overrightarrow A \, + \overrightarrow B $ will be
Given below in Column $-I$ are the relations between vectors $\vec a \,$ $\vec b \,$ and $\vec c \,$ and in Column $-II$ are the orientations of $\vec a$, $\vec b$ and $\vec c$ in the $XY-$ plane. Match the relation in Column $-I$ to correct orientations in Column $-II$.
Column $-I$ | Column $-II$ |
$(a)$ $\vec a \, + \,\,\vec b \, = \,\,\vec c $ | $(i)$ Image |
$(b)$ $\vec a \, - \,\,\vec c \, = \,\,\vec b$ | $(ii)$ Image |
$(c)$ $\vec b \, - \,\,\vec a \, = \,\,\vec c $ | $(iii)$ Image |
$(d)$ $\vec a \, + \,\,\vec b \, + \,\,\vec c =0$ | $(iv)$ Image |
If the resultant of $n$ forces of different magnitudes acting at a point is zero, then the minimum value of $n$ is
Two forces of magnitude $3\;N$ and $4\;N $ respectively are acting on a body. Calculate the resultant force if the angle between them is $0^o$