A vector is often represented by an arrow or a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online