Vector addition by the components method
In 2D Cartesian coordinates:
,
xxxx
yyyy
V ABC
VABC
V
aA bB cC
V
aA
bB
cC
V
aA
bB
cC
=±±±
⇔=±±±
⇔=
±
±
±
=
±
±
±
Example
Three forces
A
= 200 N,
B
= 100 N, and
C
= 250 N
are exerted on the pinned connector through tie rods as shown.
The total force on the pin can then be obtained as
F ABC
=++
.
(1) Express the total force vector
F
in vector notations by using unit vectors
ˆˆ
and
ij
.
(2) Find the magnitude of the total force.
(3) Also find the direction of the total force by its angle measured from the +
x
 direction
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 '09
 LYNDON
 Vector Space, Dot Product, Euclidean vector, total force, 2D Cartesian coordinates

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