1.3. LINES IN SPACE
41
and so we see that the three lines
ℓ
A
,
ℓ
B
and
ℓ
C
all intersect at the point
given by
−→
p
A
p
2
3
P
=
−→
p
B
p
2
3
P
=
−→
p
C
p
2
3
P
=
1
3
−→
a
+
1
3
−→
b
+
1
3
−→
c .
The point given in the last equation is sometimes called the
barycenter
of
the triangle
△
ABC
. Physically, it represents the
center of mass
of equal
masses placed at the three vertices of the triangle. Note that it can also be
regarded as the (vector) arithmetic
average
of the three position vectors
−→
a
,
−→
b
and
−→
c
. In Exercise
9
, we shall explore this point of view further.
Exercises for
§
1.3
Practice problems:
1. For each line in the plane described below, give (i) an equation in the
form
Ax
+
By
+
C
= 0, (ii) parametric equations, and (iii) a
parametric vector equation:
(a) The line with slope
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus

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