Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $‘n’$ times the magnitude of $(\vec A - \vec B)$. The angle between $ \vec A$ and $\vec B$ is
${\cos ^{ - 1}}\left[ {\frac{{{n^2} - 1}}{{{n^2} + 1}}} \right]$
${\cos ^{ - 1}}\left[ {\frac{{n - 1}}{{n + 1}}} \right]$
${\sin ^{ - 1}}\left[ {\frac{{{n^2} - 1}}{{{n^2} + 1}}} \right]$
${\sin ^{ - 1}}\left[ {\frac{{n - 1}}{{n + 1}}} \right]$
Two forces $P$ and $Q$, of magnitude $2F$ and $3F$, respectively, are at an angle $\theta $ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $\theta $ is ....... $^o$
The vectors $\vec{A}$ and $\vec{B}$ are such that
$|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$
The angle between the two vectors is
The vectors $\overrightarrow A $ and $\overrightarrow B$ lie in a plane. Another vector $\overrightarrow C $ lies outside this plane. The resultant $\overrightarrow A + \overrightarrow B + \overrightarrow C$ of these three vectors
Find the resultant of three vectors $\overrightarrow {OA} ,\,\overrightarrow {OB} $ and $\overrightarrow {OC} $ shown in the following figure. Radius of the circle is $R$.