PDF-Spherical Unit Vectors in relation to Cartesian Unit Vectors

can be rewritten in terms of. 1 Motivation A3 A2 Vectors A3 A21 Notational Conventions A4 A22 Visualization A5 A23 Special Vectors A5 A3 Vector Operations A5 A31 Transposition A6 A32 Equality A6 A33 Addition and Subtraction While leaving the hat off a unit vector is a nasty communic ation error in its own right it also leads one to worse mistakes such as treating vectors as if they were scalars The mathematicians have come up with a special kind of vec tor called a uni Vojin . Šenk (vojin_senk. @uns.ac.rs). Ivan Stanojević. (cet_ivan@uns.ac.rs). Mladen Kova. čević. (kmladen@uns.ac.rs). Universit. y of Novi Sad. 1. /20. Problem Formulation. Given the dimension, . A . scalar. quantity . can be described by a . single number. , . with some meaningful . unit. 4 oranges. 20 miles. 5 miles/hour. 10 Joules of energy. 9 Volts . Vectors and scalars. A . scalar. quantity . In the case of vectors, we have a special vector known as the . unit vector. Unit Vector. = any vector with a length 1; direction irrelevant . Two special unit vectors we look at the most;. i. = {1, 0}. Is a . number. with units. It can be positive or negative.. Example: distance, mass, speed, Temperature…. Chapter 3: . VECTORS. 3-2 . Vectors and Scalars. Scalar. Is a quantity with both . direction. vectors and matrices. A vector is a bunch of numbers. A matrix is a bunch of vectors. A vector in space. In space, a vector can be shown as an arrow. starting point is the origin. ending point are the values of the vector. . example:. ..  .  .  . where . are unit vectors in x, y and z directions..  . .  .  .  .  . Both, position vector of point A and point A have the same coordinates:. Vector as position vector of point A in . . example:. ..  .  .  . where . are unit vectors in x, y and z directions..  . .  .  .  .  . Both, position vector of point A and point A have the same coordinates:. Vector as position vector of point A in . Lecture 2: . Units . and . Vectors. Kinematics. Checklist. Yesterday:. Homework for Chapter 1 submitted via Mastering. Pre-lectures and check-points completed before 8:00AM today. Wednesday:. Pre-lectures and checkpoints for 1-Dim motion. Chapter 2. The stuff you should know:. Laws of Motion. Finding resultant forces. In 2D. Non-orthogonal axes. Law of Sines, Law of Cosines, Parallelogram law, Head to Tail Addition. Orthogonal. Add Cartesian Vectors(especially if more than 3 forces). Any vector can be resized by multiplying it by a real number (scalar).. Multiplying by positive scalar changes magnitude only.. Multiplying by a negative scalar changes the magnitude and its direction.. properties, addition, components of vectors . When you see a vector, think components!. Multiplication of vectors will come in later chapters.. Vectors have . magnitude. and . direction. .. Chapter 3: Vectors. Vectors Math 200 Week 1- Wednesday Math 200 Main Questions for Today What is a vector? What operations can we do with vectors? What kinds of representations and notations do we have for vectors? What are some of the important properties of vectors?