Five equal forces of $10 \, N$ each are applied at one point and all are lying in one plane. If the angles between them are equal,the resultant force will be ........... $N$.

Given that $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$ and that $\overrightarrow{C}$ is $\perp$ to $\overrightarrow{A}$. Further,if $|\overrightarrow{A}| = |\overrightarrow{C}|$,then what is the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$?

If $\vec{A} = 3\hat{i} + 4\hat{j}$ and $\vec{B} = 6\hat{i} + 8\hat{j}$,where $A$ and $B$ are the magnitudes of vectors $\vec{A}$ and $\vec{B}$ respectively,which of the following is incorrect?

If $\theta$ is the angle between two vectors $\vec{A}$ and $\vec{B}$,then match the following two columns.

Column $I$	Column $II$
$(A)$ $\vec{A} \cdot \vec{B} = |\vec{A} \times \vec{B}|$	$(p)$ $\theta = 45^{\circ}$ or $135^{\circ}$
$(B)$ $\vec{A} \cdot \vec{B} = B^2$	$(q)$ $\theta = 0^{\circ}$
$(C)$ $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$	$(r)$ $\vec{A} = \vec{B}$
$(D)$ $|\vec{A} \times \vec{B}| = AB$	$(s)$ $\theta = 90^{\circ}$

$100$ coplanar forces,each equal to $10 \ N$,act on a body. Each force makes an angle of $\pi/50$ radians with the preceding force. What is the resultant of the forces in $N$?

If $\overrightarrow{ F }=2 \hat{ i }+\hat{ j }-\hat{ k }$ and $\overrightarrow{ r }=3 \hat{ i }+2 \hat{ j }-2 \hat{ k }$,then the scalar and vector products of $\overrightarrow{ F }$ and $\overrightarrow{ r }$ have the magnitudes respectively as