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Vector Algebra - University of Utah

CHAPTER 13 Vector Basic ConceptsAvectorVin the plane or in space is an arrow: it is determined by its length, denotedjVjand itsdirection. Two arrows represent the same Vector if they have the same length and are parallel (see ). We use vectors to represent entities which are described by magnitude and direction. For example,a force applied at a point is a Vector : it is completely determined by the magnitude of the force and thedirection in which it is applied. An object moving in space has, at any given time, a direction of motion,and a speed. This is represented by the velocity Vector of the motion. More precisely, the velocity vectorat a point is an arrow of length the speed (ds=dt), which lies on the tangent line to the trajectory. Thesuccess and importance of Vector Algebra derives from the interplay between geometric interpretationand algebraic calculation.

coordinate system has been chosen: a point O, the origin, and two perpendicular lines through the origin, the x- andy-axes. A vectorV is determined by its length, j V and its direction, which we can describe by the angle θthat V makes with the horizontal (see figure 13.4). In this figure, we have realized V as the vector OP ~ from the origin ...

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