April 2015
Beginner to intermediate
208 pages
7h 31m
English
Content preview from Understanding Geometric Algebra
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Planes and lines 25
n
Π
n
l
m
l
Π
n
Π
n
l
p
O
Π
l
x
l
FIGURE 2.14 The intersection p of plane hn
Π
, xi = h and line x × m = n
l
.
normal n
l
, and the plane Π has surface normal n
Π
. Hence, their intersection line is in the
direction of n
Π
× n
l
(Fig. 2.1 4). This line intersects line l at p, the intersection point of
plane Π and line l. Choose a point x
l
on l in such a way that x
l
is parallel to n
Π
×n
l
. This
point x
l
is given by
x
l
= cn
Π
× n
l
(2.84)
for some c. Since this point satisfies the equation of line l, we have
(cn
Π
× n
l
) × m = n
l
. (2.85)
Using Eq. (2.20) of the vector triple product, the left s ide reduces to
c
hn
Π
, min
l
− hn
l
, min
Π
= chn
Π
, min
l
. (2.86)
Hence, c = 1/hn
Π
, mi
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