Distance bound from two hyperplane constraints
= Distance bound from two hyperplane constraints
{title2=$|x|geq|A-B|/|a-b|$}
If $a\ne b$ and $x\cdot a=A$, $x\cdot b=B$, the <Cauchy-Schwarz inequality> applied to $x\cdot(a-b)=A-B$ gives $\|x\|\geq|A-B|/\|a-b\|$. Equality requires $x$ parallel to $a-b$ and satisfying both original equations. The estimate gives a lower bound on the distance from the origin to the intersection; it need not be sharp if that equality condition is incompatible with the constraints.