40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Vectors Lesson: VEC-L1 Intro to VECTORS Learning Outcome B-1 VEC-L1 Objectives: Distinguish between Vectors and Scalars Draw and Label Vector quantities (magnitude, direction)

40S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Vectors Lesson: VEC-L1 A scalar quantity expresses magnitude (size) only. Example: 10 miles. A vector quantity expresses magnitude and direction. Example: 10 miles due east. Theory – Scalars and Vectors Defined

40S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Vectors Lesson: VEC-L1 Common Types of Vector A displacement vector shows the distance and direction one point is from another point. For example, 10 kilometres east of Killarney. A velocity vector shows the speed and direction that something is moving. For example, a small airplane flies west at 200 km/h. A force vector describes the force applied to an object, and the direction of the force. Force is measured in Newtons (S. I.) and pounds (American system). For example, the force applied when lifting a pail of water might be 200 N upwards. Theory – Common Types of Vector

40S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Vectors Lesson: VEC-L1 Identify the following as Scalars or Vectors A wind blowing from the west at 15 mph The number of students taking Senior 4 Applied Math at Killarney School A car travels from Treherne northeast to Portage A computer operates at a rate of 350 MHz A person walking 15 km with a bearing of 130º Example for Discussion

40S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Vectors Lesson: VEC-L1 A vector is usually illustrated using a directed line segment drawn to a convenient scale. A directed line segment is a line segment with an arrowhead on one end. This arrowhead indicates the direction of the vector quantity. The length of the line segment indicates the magnitude. The starting point of the vector is the tail of the vector and the ending point (arrowhead) is its head. Theory – Representing a Vector Visually 1 cm = 10 km/h

40S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Vectors Lesson: VEC-L1 A vector may be named in two ways. 1. A vector is labeled with letters at the head and tail as shown. 2. It is also common to label the vector with a variable. A small arrow over the variable identifies it as a vector quantity. Theory – Naming a Vector

40S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Vectors Lesson: VEC-L1 Two vectors are equal vectors if they have the same magnitude AND direction. Two vectors are collinear if they are drawn in the same line. Two vectors are opposite if they have the same magnitude and opposite directions. Theory – Equal, Collinear, and Opposite Vectors

40S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Vectors Lesson: VEC-L1 Two vectors are parallel if they have the same direction but not necessarily the same magnitude. (Collinear vectors are also parallel.) Theory – Parallel Vectors

40S Applied Math Mr. Knight – Killarney School Slide 9 Unit: Vectors Lesson: VEC-L1 The basic directions for vectors are north, east, south, and west, and are normally drawn as shown in the diagram. Other common directions such as NE, NW, SE, and SW are drawn at 45° to the basic directions. Theory – Vector Directions

40S Applied Math Mr. Knight – Killarney School Slide 10 Unit: Vectors Lesson: VEC-L1 Directions can be expressed in 3 ways: Direction of Direction: The direction of the vector shown could be written as 30° south of east, or 60° east of south. Direction Degree Direction: The direction of the vector shown could be written as E30°S. In this case, you first look east and then rotate 30° South. This direction may also be written as S60°E. Bearings: the "360° method" We can write all directions using the 360° circle, where north is 0° or 360°, east is 90°, south is 180°, and west is 270°, and all other directions are written as the appropriate number of degrees. This method is used by geographers, pilots, the military, and others. Theory – 3 Ways of Expressing Vector Direction

40S Applied Math Mr. Knight – Killarney School Slide 11 Unit: Vectors Lesson: VEC-L1 Scan and insert examples from pages B6 –B15 of FD. Theory

40S Applied Math Mr. Knight – Killarney School Slide 12 Unit: Vectors Lesson: VEC-L1 Describe the following vectors using each of the 3 methods (5+ ways to express). Example for Discussion Direction of Direction Direction Degree Direction Bearings: the "360° method"

40S Applied Math Mr. Knight – Killarney School Slide 13 Unit: Vectors Lesson: VEC-L1 To draw a vector, we must decide on a suitable scale to represent the magnitude of the vector. For example, if we draw a vector to represent a 40 km/h wind blowing in the direction E30°S, we could use the scale: 1 cm = 10 km/h. The length of the vector in the diagram is 4 cm long. We need to include the scale with the diagram. Theory – Drawing a Vector

40S Applied Math Mr. Knight – Killarney School Slide 14 Unit: Vectors Lesson: VEC-L1 Use pencil, protractor, ruler, and paper to sketch the following vectors. First determine a suitable scale to use for each vector. Then, using protractor and ruler, draw the vector the correct length and in the correct direction. Label each vector and write the scale used. A truck drives a distance of 1250 km in the direction W35ºS. An airplane flies 140 miles per hour at a bearing of 115 º. A student is walking at 7 km/h heading 20 º north of east. The student has walked for 10 minutes. Draw a displacement vector to show this change in location. Examples for Practice