LM 7_4 Vector Unit notation Collection

7.4 Unit vector notation by Benjamin Crowell, Light and Matter  licensed under the Creative Commons Attribution-ShareAlike license.

7.4 Unit vector notation (optional)

When we want to specify a vector by its components, it can be cumbersome to have to write the algebra symbol for each component:

`Deltax=290 km`, `Deltay=230 km`

A more compact notation is to write

`Deltar=(290 km)hatx + (230 km)haty,`

where the vectors `hatx`, `haty`, and `hatz`, called the unit vectors, are defined as the vectors that have magnitude equal to 1 and directions lying along the `x`, `y`, and `z` axes. In speech, they are referred to as “x-hat” and so on.

A slightly different, and harder to remember, version of this notation is unfortunately more prevalent. In this version, the unit vectors are called `hati`, `hatj`, and `hatk`:

`Deltar=(290 km)hati + (230 km)hatj.`

7.4 Unit vector notation by Benjamin Crowell, Light and Matter  licensed under the Creative Commons Attribution-ShareAlike license.