1. Vectors

2. Scalars  Consider the following objects ThermometerThermometer BeakerBeaker Battery testerBattery tester ClockClock  What do all these have in common?

3. Scalar Quantities  Any measurement that consists of a single number is a scalar. 72 °F72 °F 500 milliliters500 milliliters 1.5 volts1.5 volts 6 hours, 24 minutes (consider this as 6.4 h)6 hours, 24 minutes (consider this as 6.4 h)  Most measured quantities consist of only a single magnitude.

4. Magnitude and Direction  Position, velocity and acceleration have both a magnitude and a direction.  It takes at least two measurements to describe these values. Position on a map (N-S and E-W position)Position on a map (N-S and E-W position)  These quantities can be thought of as carrying the value from a starting point to a destination.  The word vector means carrier.

5. Vector Quantities  A measurement that requires more than one value to describe it is a vector. 80 km/h to the northwest80 km/h to the northwest 5 paces east, 3 paces south, and dig down 2 feet5 paces east, 3 paces south, and dig down 2 feet 200 m/s bearing 270° launched upwards at 30°200 m/s bearing 270° launched upwards at 30° 9.8 m/s 2 directed down9.8 m/s 2 directed down  The values within a vector measurement don’t always have the same unit, but it should be possible to convert them into the same units.

6. Vector Diagram  One representation of a vector is an arrow.  The tail shows the start of the vector.  The tip points in the direction.  The length of the arrow shows the magnitude. tail: start tip: direction length: magnitude

7.  A vector variable is represented by a small arrow over the top of the variable.  Some texts use boldface for vectors, but that can be hard to distinguish on some backgrounds. Vector Notation

8. Vectors in Equations  Vector variables can be used in equations For instance,For instance,  Vector variables are different from scalar variables They are different dimension,They are different dimension,

9. 2-D and 3-D Vectors  Some vectors have two dimensions. Two directions on a horizontal surface (boat on a lake)Two directions on a horizontal surface (boat on a lake) Vertical and one horizontal direction (ball tossed in air)Vertical and one horizontal direction (ball tossed in air)  Full motion may require three dimensions. Two horizontal and one verticalTwo horizontal and one vertical (motion of a plane circling while landing) (motion of a plane circling while landing) next