PDF-SPH3U Vectors Scalars LoRusso

In physics we are often concerned with the direction of an objects motions To represent direction we need to use vectors John was traveling at a of 100kmh compared to John was traveling at. 1 Scalars and Vectors is a number which expremay or may not have units associated with them.Examples: mass, volume, energy, money s both magnitude and direction. The magnitude of a vector is a scala Scalar quantities . have only a magnitude (amount).. Vector quantities . have a magnitude . and. a direction. . We represent them as . arrows. .. Distance. (d): . the . separation between . two . points. . 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.. 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}. 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. 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.. Motivating Question. : An Airplane flies north with an airspeed of 575 mph. If the wind is blowing 30° north of east at 50 mph, what is the speed of the plane as measured from the ground? What if the wind blew south of west?. Scalar quantities . have only a magnitude (amount).. Vector quantities . have a magnitude . and. a direction. . We represent them as . arrows. .. Distance. (d): the separation between . two points. . . 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 . In some cases, we will have to decompose a vector into a sum of two separate vectors. Recall; most vectors may be written as some variation of the special unit vectors {1,0} and {0,1}. With vectors, sometimes they may not be pointing or oriented in the proper direction. Objectives:. To describe vectors. To solve problems that involve vector addition. Vector. : .  . Any quantity with magnitude (size) and direction. . Magnitude. : . The . distance. from the initial point to the terminal point.. 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.. 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 .