LM 7_4 Vector Unit notation Collection

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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.