1 Chapter Two Vectors

2 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.

3 Vector Components See Figure 2-1. or See Figure 2-2. East: North:

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5 See Figure 2-3. See Figures 2-4, 2-5, 2-6, 2-7.

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10 Example 2-1 A box is pulled by two persons exerting the forces F 1 and F 2 shown in Fig. 2-8, which F 1 is given as 50 lb. Two questions may now be asked. 1. What force F 2 must be applied so that the box moves only in the x direction? 2. What single force could replace F 1 and F 2 so that the box moves only in the x direction?

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12 Sol See Figure 2-9. Forces on x direction: Forces on y direction:

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14 If the object is going to move in the x direction, then Question 2 can be answered as

15 Unit Vectors See Figure See Figure 2-11.

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17 Dot Product The dot product is defined as where on the right side A and B are the magnitude of each of the vectors and θ is the angle between them. See Figure 2-12.

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19 Cross Product If C is the cross product of A and B, we have and See Figure 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, Homework: 12, 16, 17.

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