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Chapter Two
Vectors
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Vectors
A quantity consisting only of magnitude is called a scalar quantity.
A quantity that has both magnitude and direction and obeys certain algebraic laws is called a vector quantity.
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Vector Components
See Figure 2-1.
or
See Figure 2-2. East: North:
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See Figure 2-3.
See Figures 2-4, 2-5, 2-6, 2-7.
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Example 2-1
A box is pulled by two persons exerting the forces F1 and F2 shown in Fig. 2-8, which F1 is given as 50 lb. Two questions may now be asked.
1. What force F2 must be applied so that the box moves only in the x direction?
2. What single force could replace F1 and F2 so that the box moves only in the x direction?
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Sol See Figure 2-9. Forces on x direction:
Forces on y direction:
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If the object is going to move in the x direction, then
Question 2 can be answered as
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Unit Vectors
See Figure 2-10. See Figure 2-11.
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Dot Product The dot product is defined as where on the right side A and B are the magnitud
e of each of the vectors and θ is the angle between them. See Figure 2-12.
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Cross Product
If C is the cross product of A and B, we have
and See Figure 2-13. The direction of C is perpendicular to both A and B and consequently perpendicular to the plane containing A and B (and obey the right-hand rule).
See Figures 2-14, 2-15. Homework: 12, 16, 17.
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