SCALARS AND VECTORS
Scalars and vectors are used in science and mathematics to represent numerical quantities. Scalars represent magnitudes or numbers without directions. Temperature and volume are examples of scalars. They only indicate how large or small a quantity is. Conversely, vectors represent quantities that need a magnitude and a direction. Velocity and displacement are examples of vector. The addition of a direction tends to make vectors slightly more involved to work with.
Scalars are simply numbers; they represent a size of a quantity. Examples of scalars include but are not limited to: temperature, work, mass, volume, pressure, or pressure.
VECTORS
Vectors require a direction and a magnitude. Not only do they tell the size of a quantity (variable), but it also indicates the way it is oriented, similar to giving directions to a far away location.
Vectors are often broken down into scalar components using a defined coordinate system. And there are other times when a vector will be expressed as a magnitude and an angle. In those situations it is often useful to sketch the vector in the coordinate system to better understand the information that is being conveyed.
TIPS
- Sketches of vectors can aid tremendously in visualizing the problem.
- As a general rule it is usually much easier to work with vectors in component form.
- Double check the sign convention. It is often the simple math errors that will cause problems with vectors and scalars.
- Does the value make sense? Mathematically? Physically?