# A vector is often represented by an arrow or a

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Unformatted text preview: 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 a vector by printing a l letter in boldface v or by putting an arrow above the letter v . For instance, suppose a particle moves along a line segment from point A to point B. The corresponding displacement vector v, shown in Figure 1, has initial point A (the tail) l and terminal point B (the tip) and we indicate this by writing v AB. Notice that the vecl tor u CD has the same length and the same direction as v even though it is in a different position. We say that u and v are equivalent (or equal) and we write u v. The zero vector, denoted by 0, has length 0. It is the only vector with no speciﬁc direction. Combining Vectors C B A FIGURE 2 l Suppose a particle moves from A to B, so its displacement vector is AB. Then the particle l changes direction and moves from B to C, with displacement vector BC as in Figure 2. The combined effect of these displacements is that the particle has moved from A to C. The l l l resulting displacement vector AC is called the sum of AB and BC and we write l AC l AB l BC In general, if we start with vectors u and v, we ﬁrst move v so that its tail coincides with the tip of u and deﬁne the sum of u and v as follows. Definition of Vector Addition If u and v are vectors positioned so the initial point of v is at the terminal point of u, then the sum u of u to the terminal point of v. v is the vector from the initial point 5E-13(pp 828-837) 1/18/06 11:10 AM Page 835 S ECTION 13.2 VECTORS ❙❙❙❙ 835 The deﬁnition of vector addition is illustrated in Figure 3. You can see why this deﬁnition is sometimes called the Triangle Law. u+v u v uv v+ u+ v v u u FIGURE 4 The Parallelogram Law FIGURE 3 The Triangle Law In Figure 4 we start with the same vectors u and v as in Figure 3 and draw another copy of v with the same initial...
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## This note was uploaded on 02/04/2010 for the course M 56435 taught by Professor Hamrick during the Fall '09 term at University of Texas at Austin.

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