Unit Vectors and Engineering Notation
Using unit vectors to represent the components of a vector
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<!--Fri Jan 20 2012 20:58:18 GMT-0500 (EST)-->
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Khan Academy
------------
Title: Unit Vectors and Engineering Notation
Description: Using unit vectors to represent the components of a vector
Url: http://www.khanacademy.org/video/unit-vectors-and-engineering-notation?playlist=Physics
InternalName: unit-vectors-and-engineering-notation
YoutubeId: 2QjdcVTgTTA
Keywords: unit, vectors, engineering
My Notes
--------
assume a vector
|| v⃗ || = 10 m/s
angle above x = 30 degrees
magnitude of the vertical component = ||v⃗_y|| = 10 * sin(30) = 5 m/s
magnitude of the horizontal component = ||v⃗_x|| = 10 * cos(30) = 5 * sqrt(3) m/s
a convention, using unit vectors
vector î "i hat" is a unit vector
it goes in the positive x direction, and its magnitude is 1
use this instead saying "to the right"
unit vector in the y direction
ĵ "j hat"
positive y direction, with magnitude 1
can write 5ĵ instead of "5 in the up direction"
we can write:
v⃗ = v⃗_x + v⃗_y = 5sqrt(3)î + 5ĵ
3 dimensions
"k hat"
unicode
--------
v⃗ is: v + ctrl-shift-u + 20d7 + space (ubuntu)
î is: ctrl-shift-u + 00ee + space (ubuntu)
ĵ is: ctrl-shift-u + 0135 + space (ubuntu)
There are no examples in this video that can be done in code.
</Notes>
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