(adsbygoogle = window.adsbygoogle || []).push({}); Consider 3D geometric algebra. Let all points on a line be given by the parametrizationx=tu+y, in which the parameter runs from minus infinity to plus infinity.

a. Show that for all points on the line we have

x(wedge)u=y(wedge)u.

b.Show that the vectordpointing from the origin onto a point on the line, such thatdhas the shortest length, satisfies

d.u=0.

c.Show no that this vectordis given by

d=(y(wedge)u)(u)^(-1).

d.Given two lines given by parametrizations

su1+y1and

ru2+y2,

where the parameters s and r run from minus to plus infinity.

Show that for the two lines to have an intersection we must have that

(y1-y2)(wedge)(u1-u2)

is proportional to

u1)(wedge)(u2.

I posted this because i wanted help first plotting the parametrization and i figured ill be asking questions about the rest of it later, thus i typed out the whole problem. I realize this plotting is hard to explain on an internet thread, but maybe some tips?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 3D Geometric Algebra

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**