What are unit vectors exactly?

I know the definition ("dimensionless" vectors with unit magnitude) but I don't quite understand how to recognize them. I was given this list:





%26lt;0, -1, -1%26gt;


%26lt;0.9, 0, 0.1%26gt;


%26lt;1, 1, 1%26gt;


%26lt;0, -1, 0%26gt;


%26lt;0, 1, 0%26gt;


%26lt;0.333, 0.333, 0.333%26gt;


%26lt;0.5, 0.5, 0%26gt;


%26lt;0.577, -0.577, 0.577%26gt;


%26lt;0.372, -0.557, 0.743%26gt;


%26lt;1, 0, 0%26gt;


%26lt;3,0,0%26gt;


%26lt;0.949, 0, -0.316%26gt;


%26lt;0, 0, -1%26gt;





But I don't know how to pick them out.





And while I'm here I've got another question too.





Are the components of C = A + B necessarily larger than the corresponding components of either A or B?

What are unit vectors exactly?
Do you know how to calculate the length of a vector when given its (x,y) or (x,y,z) coordinates???





Just calculate the lengths of each of those vectors - and if their length is 1 - then you have a unit vector.





for example: (1,0,0) is only 1 long.





(0, -1, -1) is the square root of 2 long - so it is not a unit vector.





What is the square root of .940 squared pluse .316 squared??? If it is one - then (0.949, 0, -0.316) is a unit vector.