Answer:
Yes. The "direction to the Sun" is the same for everyone on the beach. It is a vector.
Yes. The "direction to the Sun" is the same for everyone on the beach. It is a vector.
Sometimes (as in the question) we are interested only in direction, not location, nor length. Use a vector for this. Its length does not matter. Often a length of one is used.
Other times we are interested in both direction and magnitude. Then both the direction and length of the vector are used.
A vector may be represented with a list of numbers called a column matrix. A column matrix is an ordered list of numbers written in a column.
Some books use the word "vector" to mean both the idea of a vector and its representation as an arrangement of three numbers. This sometimes can be confusing. Here is an example of a column matrix:
Each number of the column matrix is called an element. The numbers are real numbers. The number of elements in a vector is called its dimension. A row matrix is an ordered list of numbers written in a row. Here is an example of a row matrix:
(12.5, -9.34)
To be consistent, our vectors will always be represented with column matrices. Some books represent vectors with row matrices, which makes no fundamental difference, but slightly changes some mathematical formulas.
