Vectors

A vector is a type of variable that includes information about direction as well as size. Unlike words such as “right” and “left,” a vector includes direction information in a specific mathematical way so that vectors in different directions can be added, subtracted, or multiplied.
Vectors and scalars A scalar does not depend on direction and can be completely specified with a single value. Distance, mass, and temperature are scalar variables. A distance can be zero, or any number of meters but a distance cannot be negative! The distance between two points can always be represented by a single value. The same is true of mass and temperature.
Displacement is a vector even though distance is not. A displacement of 10 meters tells you to move 10 meters to the right in the coordinate system of the diagram below. A displacement of −10 meters is a movement of ten meters to the left. With a vector, the positive and negative signs carry direction information.
Displacement is a vector
The magnitude of a vector is its “length” independent of its direction. The displacements of +10 m and −10 m both have a magnitude of 10 m. The distance is the magnitude of the velocity vector. The magnitude of a vector can either be zero or have a positive value, such as 10 m. Magnitude cannot be negative.
A map as a two-dimensional coordinate system A map is a two-dimensional surface which has length and width. The north-south axis provides one perpendicular reference line, usually called the y-axis. The east-west axis provides the second perpendicular reference line, usually called the x-axis. Using these two axes, every point on the surface can be uniquely identified with two numbers, x and y. A map is two-dimensional because it takes two numbers to uniquely specify any point. An important use for vectors is for navigation, which involves using maps to know where you are, and to plan and carry out movements.
Is density an example of a vector or scalar quantity? Show


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