Two Perpendicular Unit Vectors

★ 7/10Substitutionvectors

Problem

In the plane, AB1→⋅AB2→=0\overrightarrow{AB_1} \cdot \overrightarrow{AB_2} = 0, ∣OB1→∣=∣OB2→∣=1\left|\overrightarrow{OB_1}\right| = \left|\overrightarrow{OB_2}\right| = 1, and AP→=AB1→+AB2→\overrightarrow{AP} = \overrightarrow{AB_1} + \overrightarrow{AB_2}. If ∣OP→∣<12\left|\overrightarrow{OP}\right| < \dfrac12, find the range of ∣OA→∣\left|\overrightarrow{OA}\right|.

Answer

Solution

Difficulty7/10
TopicsSubstitution, vectors

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