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If a vector also has a length, why is it perceived to be of 3 values?


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Because the three values defines an imaginary line going from 0,0,0 to the position in space described by the 3 values. That point can be far away or i can be close to 0,0,0. This way the 3 values are able to define both a direction and a length.


Edited by bonsak
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There's ways to decompose/describe a vector

- 3 coordinates (xyz) that scale the coordinate system unit vectors (ijk) and add them together:  P = i*x + j*y + k*z.

- direction (vector scaled to length 1) and legth/magnitude (distance from tail to head of the vector)

- direction (two angles) and length

And more...

It's all about using the representation that is more sensible to the operation you are doing. For angular related calcs direction is handy, while for position calcs you want to deal with xyz, etc.

Edited by probiner
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