Let $\theta$ be the angle between vectors $\vec{A}$ and $\vec{B}$. Which of the following figures correctly represents the angle $\theta$?

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 $\overrightarrow {AO}$?

The angle subtended by the vector $\vec{A} = 4 \hat{i} + 3 \hat{j} + 12 \hat{k}$ with the $x$-axis is

$A$ unit vector is given by $a\hat{i} + b\hat{j} + c\hat{k}$. If the values of $a$ and $b$ are $0.6$ and $0.8$ respectively, find the value of $c$.

What is the minimum number of coplanar vectors of different magnitudes whose sum can be zero?

The unit vector along $\hat{i} + \hat{j}$ is