If a vector is a combination of two unit vectors, is this vector still a unit vector?
For example $\vec v_1$ and $\vec v_2$ are both unit vectors, that is, their lengths are both $1$.
Now if there is a vector $\vec f$.
$\vec f=\alpha \vec v_1+(1-\alpha )\vec v_2$ , $ 0<\alpha<1$
Is $\vec f$ also a unit vector?