Two forces of $10 \,N$ and $6 \,N$ act upon a body. The direction of the forces are unknown. The resultant force on the body may be .........$N$

A vector $\vec A $ is rotated by a small angle $\Delta \theta$ radian $( \Delta \theta << 1)$ to get a new vector $\vec B$ In that case $\left| {\vec B - \vec A} \right|$ is

Find the resultant of three vectors $\overrightarrow {OA} ,\,\overrightarrow {OB} $ and $\overrightarrow {OC} $ shown in the following figure. Radius of the circle is $R$.

The vector that must be added to the vector $\hat i - 3\hat j + 2\hat k$ and $3\hat i + 6\hat j - 7\hat k$ so that the resultant vector is a unit vector along the $y-$axis is

If the angle between $\hat a$ and $\hat b$ is $60^o$, then which of the following  vector $(s)$ have magnitude one

$(A)$ $\frac{\hat a + \hat b}{\sqrt 3}$     $(B)$ $\hat a + \widehat b$     $(C)$ $\hat a$      $(D)$ $\hat b$

What is the angle between $\overrightarrow P $ and the resultant of $(\overrightarrow P + \overrightarrow Q )$ and $(\overrightarrow P - \overrightarrow Q )$