A Range of a Vector-Coefficient Expression

★ 7/10Substitution Completing the Square analytic geometry vectors

Problem

In the coordinate plane $xOy$ , let $A,B,C$ be distinct points on the circle $x^2+y^2=1$ . If there exist reals $\lambda,\mu$ with $\overrightarrow{OC}=\lambda\overrightarrow{OA}+\mu\overrightarrow{OB}$ , find the range of

(\lambda-3)^2+\mu^2.

Answer

Solution

Difficulty	7/10
Topics	Substitution, Completing the Square, analytic geometry, vectors

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