Angle Between Two Planes in a Unit Tetrahedron

★ 6/10solid geometry Linear Algebra vectors

Problem

As shown in the figure, in a regular tetrahedron $ABCD$ with edge length $1$ , points $M$ , $N$ , $K$ lie on edges $AB$ , $AD$ , $BD$ , respectively, with

BM = DN = \dfrac{1}{3}, \qquad DK = \dfrac{1}{4}.

Find the cosine of the acute angle between plane $ACK$ and plane $CMN$ .

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.