Unit Vectors at $120^\circ$

★ 6/10Substitution algebra AM-GM vectors

Problem

Unit vectors $\vec e_1, \vec e_2$ make an angle of $120^\circ$ , and reals $x, y$ satisfy

\left|x\vec e_1 + y\vec e_2\right| = \sqrt3.

Find the range of $\left|x\vec e_1 - y\vec e_2\right|$ .

Answer

Solution

Difficulty	6/10
Topics	Substitution, algebra, AM-GM, vectors

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments