A Sum of Two Moving Lengths

★ 8/10ExtremaParametrizationvectors

Problem

Plane vectors a,b,c\boldsymbol a,\boldsymbol b,\boldsymbol c satisfy

2∣a∣=∣b∣=2∣c∣=2,a⋅b=1.2|\boldsymbol a|=|\boldsymbol b|=2|\boldsymbol c|=2,\qquad \boldsymbol a\cdot\boldsymbol b=1.

Find the range of

∣a+2c∣+∣b−c∣.|\boldsymbol a+2\boldsymbol c|+|\boldsymbol b-\boldsymbol c|.

Answer

Solution

Difficulty8/10
TopicsExtrema, Parametrization, vectors

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