Two forces $3\,N$ and $2\,N$ are at an angle $\theta$ such that the resultant is $R$. The first force is now increased to $6\,N$ and the resultant becomes $2R$. The value of $\theta$ is ....... $^\circ$.

Six vectors,$\overrightarrow a$ through $\overrightarrow f$,have the magnitudes and directions indicated in the figure. Which of the following statements is true?

With respect to a rectangular cartesian coordinate system,three vectors are expressed as $\vec a = 4\hat i - \hat j$,$\vec b = -3\hat i + 2\hat j$,and $\vec c = -\hat k$,where $\hat i, \hat j, \hat k$ are unit vectors along the $X, Y,$ and $Z$-axis respectively. The unit vector $\hat r$ along the direction of the sum of these vectors is:

When $n$ vectors of different magnitudes are added,we get a null vector. Then the value of $n$ cannot be

Two vectors having equal magnitudes $A$ make an angle $\theta$ with each other. The magnitude and direction of the resultant are respectively

The magnitudes of vectors $\vec A, \vec B$ and $\vec C$ are $3, 4$ and $5$ units respectively. If $\vec A + \vec B = \vec C$,the angle between $\vec A$ and $\vec B$ is