The vectors $(A + B)$ and $(A - B)$ are at right angles to each other. This is possible under the condition

If a unit vector is represented by $0.5\hat i + 0.8\hat j + c\hat k$,then the value of $c$ is

Find $|\Delta \overrightarrow{a}|$ and $\Delta a$ when a vector $\overrightarrow{a}$ is rotated by an angle $d\theta$.

The five sides of a regular pentagon are represented by vectors $A_1, A_2, A_3, A_4$ and $A_5$ in cyclic order as shown in the figure. Corresponding vertices are represented by vectors $B_1, B_2, B_3, B_4$ and $B_5$,drawn from the center of the pentagon. Then,$B_2 + B_3 + B_4 + B_5$ is equal to:

The resultant magnitude of two vectors of same magnitude is equal to the magnitude of either. The angle between the two vectors is (in $^{\circ}$)

If $\vec{A}$ and $\vec{B}$ are two non-zero vectors such that $|\vec{A} + \vec{B}| = \frac{|\vec{A} - \vec{B}|}{2}$ and $|\vec{A}| = 2|\vec{B}|$,then the angle between $\vec{A}$ and $\vec{B}$ is