ME
–
210
Applied Mathematics for Mechanical Engineers
Prof. Dr. Faruk Arınç
Spring 2010
Equations of Lines and Planes in 3-D Space
Straight Lines
Consider the straight line, L. passing through a
given point P
1
(x
1
, y
1
, z
1
,) and parallel to a given
vector
. For any point, P(x, y, z)
on the straight line:
1
1
1
1
PP = t V =
x - x
i +
y - y
j +
z - z
k = t
a i + b j + c k
where t is any non-zero scalar.
V = a i + b j + c k
V
1
P
P
1
1
1
x - x
= t a
y - y
= t b
z - z = t c
are the parametric equations of the straight line, L. This can
be written as
1
1
1
x - x
y - y
z - z
=
=
= t
a
b
c

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