ME 214 Vector Statics
Lecture 4, Chapter 2.112.15
Instructor: A Rezaei
Today’s Objective: Students will be able to:
a) Represent a position vector in Cartesian coordinate form, from given
geometry.
b) Represent a force vector directed along a
line.
c) determine an angle between two vectors,
and,
d) determine the projection of a vector along
a specified line.
POSITION VECTOR
The position vector directed from A to B
,
r AB
, is defined as
r AB
=
{( X
B
–
X
A
)
i
+
( Y
B
–
Y
A
)
j
+
( Z
B
–
Z
A
)
k
}m
Please note that B is the ending point and A is the starting point.
So ALWAYS subtract the “tail” coordinates from the “tip”
coordinates!
FORCE VECTOR DIRECTED ALONG A LINE
a) Find the position vector,
r
AB
, along two points on that line.
b) Find the unit vector describing the line’s direction,
u
AB
= (
r
AB
/r
AB
).
c) Multiply the unit vector by the magnitude of the force,
F
=
F
u
AB
.
EXAMPLE 1
Given:
400 lb force along the cable DA.
Find:
The force
FDA
in the Cartesian vector form.
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 Summer '06
 Lipovetsky
 Statics, Vector Space, Dot Product, Force, Euclidean vector

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