PPT-Chapter 12 Vectors and the Geometry of Space

Section 121 ThreeDimensional Coordinate Systems Section 122 Vectors Section 123 The Dot Product Section 124 The Cross Product Section 125 Lines and Planes in Space Section 126 Cylinders and . 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 define . scalar and vector quantities and . give . examples.. (. b) draw and use a vector triangle to . determine the resultant of two vectors such as displacement, velocity and force.. (c) Use trigonometry to determine the resultant of two vectors.. A.S. 1.3.1 – 1.3.4. Scalar Quantities. Those values, measured or coefficients, that are complete when reported with only a magnitude. Examples:. . the table is 2.5 m long. . He ran the 100. m race in 12.65 s.. Section 3.4. Bases for Subspaces. Spanning Sets. Let . W. be a subspace of . , and . a set of vectors in . W. (. i.e. . ). The set . S. is a . spanning set . for . W. (or . S. . spans. . W. ) if and only if every vector in . 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 . At the end of yesterday, we addressed the case of using the dot product to determine the angles between vectors. Similar to equations from algebra, we can talk about relationship of vectors as well. Parallel. GENETIC. . ENGINEERING. Genetic engineering is the manipulation of genetic materials which can be introduced in the host organisms and thus change the phenotype of the host organism.. Distinguish between scalars and vectors.. Recognise quantities as either scalars or vectors.. HL: Find the resultant of perpendicular vectors.. HL: Describe how to find the resultant of two vectors.. Scalar. A . SCALAR. is ANY quantity in physics that has . MAGNITUDE. , but NOT a direction associated with it.. Magnitude. – A numerical value with units.. Scalar Example. Magnitude. Speed. 20 m/s. Anthony Bonato. Ryerson University. 1. st. Symposium on Spatial Networks. Oxford University. 1. Friendship networks. network of on- and off-line friends form a large web of interconnected links. 2. Geometry of Social Networks. John . Cadigan. , David Ellison, Ethan Roday. System Overview. Document summarization system is organized as a multi-step pipeline.. System Overview. Two major components for content selection:. Feature selection step to generate sentence vectors. Take your name card from the table. Place it on your desk with your name facing the . instructor. Fill out the information form that is on your . desk . Sit quietly. Honors Geometry. Dr. Alan L. . Breitler. Does space exist?. What is the relation between a theory and reality?. Views of Reality: a spectrum. The common person. There are definite events independent of observation. Our senses record these events. Theories can represent genuine causal patterns inherent in the events. Generally, the features we use to describe things, e.g. size, time…, are inherent in the events themselves. The world consists of collections of 'things'.. Examples should include: . velocity/speed, mass, force/weight, acceleration, displacement/distance. . Addition of vectors by calculation or scale drawing. . Calculations will be limited to two vectors at right angles. Scale drawings may involve vectors at angles other than .