(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?

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# 3D Geometric Algebra

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