Six Angles with a Box

★ 6/10solid geometry Linear Algebra vectors

Problem

A plane $\alpha$ makes angles $\theta_i$ ( $i = 1, 2, \dots, 6$ ) with the six faces of a rectangular box. Find the value of

\sum_{i=1}^{6}\sin^2\theta_i.

Answer

Solution

Difficulty	6/10
Topics	solid geometry, Linear Algebra, 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

No comments yet.