Vectors
Vectors is a directed line segment. (such as displacement, velocity or
force) that has both magnitude and direction. A vector is often
represented by an arrow or a directed line segment. The length of
the arrow represents the magnitude of the vector and the arrow
points in the direction of the vector. We denote the vector by
In Fig. 1 A and C are the initial point, B and D are the terminal point
The vector u has the same length and the
same direction as v even though it is in a
different position. We say that and are
equivalent (or equal) and we write u = v.
The zero vector denoted by 0, has length 0.1
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Definitions
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Theorem
Proof:
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Unit Vector
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Theorem
Proof:
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(b)
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2.9 Equilibrium of a particle
When the resultant of all the forces acting on a particle is zero, the particle is in equilibrium.
we write
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PROBLEMS
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Forces in space
2.12 Rectangular components of a force in space
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2.13 Force defined by its magnitude and two points on its line of action
Consider the vector MN joining M and N
We write
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The unit vector  along the line of action of F. We write
Recalling that F is equal to the product of F and , we have
from which it follows that the scalar components of F are, respectively,
where
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The angles
In the space
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2.15 Equilibrium of a particle in space
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