MathDB

Consider a (right) square pyramid

ABCDV

with the apex

V

and the base (square)

ABCD

. Denote

d=AB/2

and

\varphi

the dihedral angle between planes

VAD

and

ABC

. (1) Consider a line

XY

connecting the skew lines

VA

and

BC

, where

X

lies on line

VA

and

Y

lies on line

BC

. Describe a construction of line

XY

such that the segment

XY

is of the smallest possible length. Compute the length of segment

XY

in terms of

d,\varphi

. (2) Compute the distance

v

between points

V

and

X

in terms of

d,\varphi.

Problem Statement