Having two vectors $a$ and $b$ and with $b$ fixed, how would I go about increasing the angle between the two vectors by a specified $\Delta \theta$?
The dot product equation:
$$ a \cdot b = |a| \cdot |b| \ \cos \theta .$$
gives multiple solutions in the form of a cone for $3$-dimensional vectors. I want the new vector $a'$ to be in the same plane spanned by $a$ and $b$.
Also can this case be extended to arbitrary number of dimensions?