Surface area is

The figure shows $ABCDEF$ as a regular hexagon. What is the value of $\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} + \overrightarrow {AE} + \overrightarrow {AF}$ in terms of $\overrightarrow {AO}$?

Given that $\overrightarrow A + \overrightarrow B + \overrightarrow C = 0$. Out of three vectors,two are equal in magnitude and the magnitude of the third vector is $\sqrt{2}$ times that of either of the two having equal magnitude. Then the angles between the vectors are given by:

$A$ vector $\overrightarrow{a}$ is turned without a change in its length through a small angle $d\theta$. The values of $|\Delta \overrightarrow{a}|$ and $\Delta a$ are respectively:

A body cools from $100^\circ C$ to $60^\circ C$ in $20$ minutes, the temperature of the surroundings being $20^\circ C$. The total time taken (in minutes) for the body to cool down to $40^\circ C$ is ...

If a vector $\overrightarrow{P}$ makes angles $\alpha, \beta,$ and $\gamma$ with the $X, Y,$ and $Z$ axes respectively,then $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = $