A Max Scalar Projection

Problem

In the plane, $\boldsymbol e_1$ and $\boldsymbol e_2$ are perpendicular unit vectors. A vector $\boldsymbol a$ satisfies $|\boldsymbol a-4\boldsymbol e_1|=2$ , and a vector $\boldsymbol b$ satisfies $|\boldsymbol b-6\boldsymbol e_2|=1$ . Find the maximum value of the scalar projection of $\boldsymbol b$ onto the direction of $\boldsymbol a$ .

Answer

Solution

Difficulty	6/10
Topics	Extrema, Circles, vectors

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