Hello, classicstrings!

I drew a sketch for #2 . . . and saw an "eyeball" solution!

$\displaystyle \text{2. The angle between vectors }\vec{a}\text{ and }\vec{b}\text{ is }120^o,\;\text{ and }|a| = |b|.$

$\displaystyle \text{Find the angle between }\vec{a}\text{ and }\overrightarrow{a + b}$ Code:

*
* *
* *
b * * a+b
* *
* 120* *
* * * * * * * * * *
a

We are given: The angle between $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$ is $\displaystyle 120^o$ and $\displaystyle |a| = |b|.$

We have an __isosceles__ triangle with equal sides $\displaystyle |a|$ and vertex angle $\displaystyle 120^o.$

Therefore, the base angles are $\displaystyle 30^o.$