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Main » Kinematics & Dynamics » Vector & Scalar Quantities » Lesson I.2.1

Scalar and Collinear Vectors - Lesson I.2.1

 Key Terms: scalar quantity | vector quantity | vector | collinear vectors | equivalent vectors | resultant vector |

 We are already familiar with some scalar quantities such as mass (6 kg), time (3 s) and distance (2 km). After examining the similarities in these examples you should notice that scalar quantities consist of a magnitude ( a number and a unit). In order to add scalar quantities your units must be the same.
 i.e. if you were to add 12 min to 2 hr you would have to convert hours to minutes or vise versa.

 On the other hand, vector quantities consist of a magnitude and a direction (32 m [N]). Because of the need for a direction, vector quantities are able to describe various aspects of kinematics and dynamics. Position, displacement, and velocity are all examples of vector quantities.

 Vectors are used to represent vector quantities on a diagram. A vector is composed of a line segment drawn to scale with an arrowhead at one end. The tail of the vector is at its origin and the tip is at the terminal point (the arrowhead). The length of the vector represents its magnitude and the arrowhead indicates its direction. When drawing vectors you must also include reference coordinates.
 Reference Coordinate

Collinear vectors are vectors that exist in the same dimension. In other words, they exist either in the same direction or in the opposite direction.

Special types of collinear vectors are equivalent vectors. These vectors are equal in magnitude and direction.

The direction of a vector is always expressed in square brackets in one of two forms.

1. One of the four basic directions: north, south, east, or west.
2. Relative to a north or south position such that the degrees is less than 90.

Note: The tail is always located at the origin of an imaginary Cartesian plane

Vectors can be added algebraically if the directions are the same or if you can make them the same with the addition of a minus sign.
6 cm [W] = -6 cm [E]
The negative vector quantity indicates that its direction is actually opposite to that stated. In this example, the object is actually moving 6 cm west.

The vector sum of two or more vectors is called the resultant vector. Now, determine the resultant vector for the following.