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distance of perpendicular lines, regular hexagonal prism

Source: 2013 Romania District VIII P3

May 19, 2020

prism3D geometrygeometryperpendicular

Problem Statement

Let be the regular hexagonal prism

ABCDEFA'B C'D'E'F'

with the base edge of

12

and the height of

12 \sqrt{3}

. We denote by

N

the middle of the edge

CC'

.
a) Prove that the lines

BF'

and

ND

are perpendicular
b) Calculate the distance between the lines

BF'

and

ND