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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.
A vector is a quantity that has both direction and magnitude. Let a vector be denoted by the symbol . A. The magnitude of . A. is | A| ≡. A . We can represent vectors as geometric objects using arrows. The length of the arrow corresponds to the magnitude of the vector. The arrow points in the direction of the vector (Figure 3.1). 1 . Galileo ...
triangle law of addition, assigns meaning to Eq. (1.1) and is illustrated in Fig. 1.1. By completing the parallelogram, we see that C =A +B =B +A, (1.2) as shown in Fig. 1.2. In words, vector addition is commutative. For the sum of three vectors D =A +B +C, Fig. 1.3, we may first add A and B: A +B =E. 1
Depictions of geometric angles will look like the one shown in this figure: s 1 s 2 V Figure 1.1.1 The above figure depicts a non-flat geometric angle \s 1s 2, with vertex V. The flat angles are: the straight angles, whose sides are opposite “halves” of a line; the trivial angles, whose sides coincide. Any non-flat angle \s 1s
Structures and analytical geometry of curves and surfaces is covered in detail. The second unit discusses algebra of operators and their types. It explains the equivalence between the algebra of vector operators and the algebra of matrices. Formulation of eigenvectors and eigenvalues of a linear vector operator are discussed using vector algebra.
Vector Geometry. 4.1 Vectors and Lines. In this chapter we study the geometry of 3-dimensional space. We view a point in 3-space as an arrow from the origin to that point. Doing so provides a “picture” of the point that is truly worth a thousand words.
VECTOR GEOMETRY. 1.1 INTRODUCTION. In this chapter vectors are first introduced as geometric objects, namely as directed line segments, or arrows. The operations of addition, subtraction, and multiplication by a scalar (real number) are defined for these directed line segments.
