PPT-Vectors and Scalars

Objectives Distinguish between vector and scalar quantities Add vectors graphically Scalar a quantity that can be completely described by a number called its magnitude and a unit Ex length temperature and volume. 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 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.. 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}. 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. vs. Vectors. Scalars – a quantity that only needs a magnitude (with a unit) to describe it. . Ex:. . Vectors – a quantity that needs a magnitude (with a unit) and a direction to completely describe it. Any vector can be resolved into horizontal and vertical components. v. v. x. v. y. A Helicopter is traveling . above a highway at . 29m/s at an angle of 25 degrees with respect to flat ground.. . How fast would a sports car have to travel to stay beneath the helicopter?. Matrices. Definition: A matrix is a rectangular array of numbers or symbolic elements. In many applications, the rows of a matrix will represent individuals cases (people, items, plants, animals,...) and columns will represent attributes or characteristics. 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.. . 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 . 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. 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. Vectors, Shmectors. Objectives. 1. Distinguish between a scalar and a vector.. 2. Add and subtract vectors by using the graphical method.. 3. Multiply and divide vectors by scalars.. Vectors, Schmectors. In physics, we are often concerned with the direction of an object's motions. To represent direction we need to use vectors. "John was traveling at a of 100km/h" compared to "John was traveling at 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 .