Range of $\lambda + \mu$ for a Point on a Quarter Arc

★ 7/10Extrema Parametrization inequality vectors

Problem

As shown in the figure, in square $ABCD$ , $E$ is the midpoint of side $AB$ , and $P$ is a point on the circular arc from $B$ to $D$ centered at $A$ with radius $AB$ (endpoints included). Given that

\overrightarrow{AC} = \lambda \overrightarrow{DE} + \mu \overrightarrow{AP},

find the range of $\lambda + \mu$ .

Answer

Solution

Difficulty	7/10
Topics	Extrema, Parametrization, inequality, vectors

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