Vectors and Scalars Are Your Friends for Life
Vectors and scalars are two mathematical ideas that are used all the time in math and science. The most basic of the two is a scalar. A scalar is just a number – a quantity. That’s it! So, if I had 3 cats, 2 dogs, and 5 birds, the 3, 2, and 5 are all scalar values. A vector, on the other had, is a scalar and a direction. Vectors can be represented as an arrow where the length of the arrow represents the size of the scalar value associated with the vector. So, if a boat was traveling due west at 15 knots we could represent that with an arrow with length of 15 units pointing due west (270 degrees).
Imagine two vectors (arrows) drawn on a sheet of paper. Without changing the length or direction of the arrows (vectors), we are allowed to move the vectors anywhere on the sheet of paper. Vectors are moveable.
We already know how to add scalars. 2 +3 = 5. Adding vectors is easy too! The image above is adding vectors a and b. To do this we place the tail end of one vector at the head of the second vector. The sum is the vector from the tail of the first vector to the head of the second vector. The order of adding the two vectors doesn’t matter; the sum is the same. Again. please see the above image. Notice how the sum vector has a new direction. This new vector is a blend between the vectors that were added.
For more on vectors visit Vectors.