Feasible inner products with two unit vectors
= Feasible inner products with two unit vectors
For linearly independent unit vectors $y,z$ with $c=y\cdot z$, a pair
$$
p=x\cdot y,\qquad q=x\cdot z
$$
is attained by some unit vector $x$ exactly when
$$
\frac{p^2-2cpq+q^2}{1-c^2}\leq1.
$$
The left-hand side is the squared norm of the least-norm vector having those two inner products.