Vectors
Key Questions
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A vector
vecv can be represented as a pointed arrow drawn in space:The length of the arrow (relative to some kind of reference or scale) represents the relative magnitude of the vector while the arrow head gives us the direction in which the vector operates.
Another way to represent a vector is by giving its components .
Basically, in space, you choose three unit vectors ( of magnitude1 and directions the positive ones of thex,y and z axes) indicated asveci, vecj and veck and then you do a linear combination of these three unit vectors using three components (=numbers such as5,4 and 6 ).For example,
vecu=5veci+4vecj+6veck Basically you can think of it as a recipe of a cake where
veci, vecj and veck are the ingredients:
To "make" vectorvecu you need to mix (=combine linearly):
5 units of ingredientveci ;
4 units of ingredientvecj ;
6 units of ingredientveck .