 ## Vectors

If someone told you that a car drove five miles from the point where you are standing now, could you tell me precisely where the car is? Certainly not, to be more precise he/she should have spoken of which direction the car was traveling. For example, five miles south of where you are standing. What if I took your temperature with a thermometer and it read 37.0 °C? Would I need anything else to explain your temperature precisely? Certainly not, so as you can see it turns out that certain quantities, in order to be precisely defined, need to be expressed in terms of a number or magnitude (such as five miles, or 98.6 °F) as well as a direction ([five miles] south). In physics (and mathematics) we call quantities that need both a magnitude and direction a vector quantity. We also call a quantity that needs only a magnitude a scalar quantity. Notice that physicists say a vector or scalar quantity. These are terms we use to apply to certain quantities in nature. For example, a force such as a push or pull, needs both a magnitude as well as a quantity. Why? Forces involve how much or to what degree an object is being pushed or pulled and in what direction. Thus we can say a force is a vector quantity. How about a quantity such as mass? Do you think the mass of an object needs both a magnitude and direction to precisely describe it? Absolutely not. Thus we can say that the quantity mass is a scalar quantity. Physicists have many ways at their disposal to account for direction. Notice in the vector example above we used the cardinal direction, south. It could also have been equally proper to say that the car traveled a distance of 5 miles at 270°. Here we are using what is known as polar coordinates. Polar coordinates are standardized so that everyone knows where a particular degree is. The direction facing North is 90ş. 0ş/360ş is East, etc. It is also possible to express the displacement of the car in terms of an equation using unit vectors (Unit vectors are dimensionless and express a particular direction. In this case the x, y, z directions are labeled i, j, k, respectively.):

```	A = -5i + 0j + 0k
```

What do you think the minus sign is used for? The minus sign "operates" or tells the vector it is applied to, to change its direction by 180ş.