Dot Product of Two Vectors

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors of magnitude $2$ and inclined at an angle $60°$, then angle between $\overrightarrow{a}$ and $\overrightarrow{a}+\overrightarrow{b}$ is

If $a, b, c$ are three-zero vectors such that each one of them are perpendicular to the sum of the other two vectors, then the value of $|\mathrm{a}+\mathrm{b}+\mathrm{c}{|}^2$ is

The sin of the angle between the vectors $3\hat{i}+\hat{j}+2\hat{k}$ and $\hat{i}+\hat{j}+2\hat{k}$ is