Αποτελέσματα Αναζήτησης
We defined a vector in Rn as an n-tuple, i.e., as an n×1 matrix. This is an algebraic definition of a vector where a vector is just a list of num-bers. The geometric objects we will look at in this chapter should be seen as geometric interpretations of this alge-braic definition.
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.
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.
Triangle rule: Put the second vector nose to tail with the first and the resultant is the vector sum. b. = c=a+b. (the parallelogram rule. I c = a + b : in (x; y; z) components. is completely. (cx; cy; cz) = (ax+bx; ay +by; az+bz) analagous) I Alternatively c = a + b.
1. Definition of vectors. Vectors are usually indicated by boldface letters, such as A, and we will follow this most common convention. Alternative notation is a small arrow over the letters such as. . A . The magnitude of a vector is also often expressed by A A . The displacement vector serves as a prototype for all other vectors.
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.
1 Vectors: Geometric Approach. What's a vector? in elementary calculus and linear algebra you probably de ned vectors as a list of numbers such as ~x = (4; 2; 5) with special algebraic manipulations rules, but in elementary physics.
