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are then called rectangular components. For analytical work we can
represent these components in one of two ways, using either scalar
notation or Cartesian vector notation.
Scalar Notation. The rectangular components of force F shown
in Fig. 1-1 are found using the parallelogram law, so that F = F x + F .
y
Because these components form a right triangle, their magnitudes can
be determined from F = F cosθ and F = F sinθ .
x
y
a b
Fig. 1-1.
Instead of using the angle, however, the direction of F can also
be defined using a small “slope” triangle, such as shown in Fig. 1-1,b.
Since this triangle and the larger shaded triangle are similar, the
proportional length of the sides gives
F x = a 1-1
F c
or
a
F = F 1-2
x
c
and
F y = b 1-3
F c
or
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