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