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A vector is a quantity that has both a magnitude (or size) and a direction. Both of these properties must be given in order to specify a vector completely. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry.
Triangle Law for finding the resultant of two vectors: If 2 vectors are drawn head to tail, the vector from the tail of the first to the head of the second is the resultant. Parallelogram Law for finding the resultant of two vectors: If 2 vectors, drawn tail to tail, are the adjacent sides ab and ad of a parallelogram abcd, the
Three numbers are needed to represent the magnitude and direction of a vector quantity in a three dimensional space. These quantities are called vector quantities. Vector quantities also satisfy two distinct operations, vector addition and multiplication of a vector by a scalar.
1 Algebraic operations with vectors. 119. Definition of vectors. In physics, some quantities (e.g. distances, volumes, temperatures, or masses) are completely charac-terized by their magnitudes, expressed with respect to a chosen unit by real numbers. These quantities are called scalars.
Triangle Law of Vector Addition is used to add two vectors when the first vector's head is joined to the tail of the second vector and then joining the tail of the first vector to the head of the second vector to form a triangle, and hence obtain the resultant sum vector.
A vector V in the plane or in space is an arrow: it is determined by its length, denoted V and its direction. Two arrows represent the same vector if they have the same length and are parallel (see figure 13.1). We use vectors to represent entities which are described by magnitude and direction.
3 VECTORS 1. Objectives. After studying this chapter you should. • understand that a vector has both magnitude and direction and be able to distinguish between vector and scalar quantities; • understand and use the basic properties of vectors in the context of position, velocity and acceleration; • be able to manipulate vectors in ...
