Posted 3 March 2011 - 01:39 AM
Posted 3 March 2011 - 01:49 AM
In terms of the magnitude of a unit vector (or any vector) it relates to size.
A vector is something that carries two pieces of information, direction and size. So 3km east is a vector, or 1 Newton down. We often use unit vectors when we are supplying the size information elsewhere so we'll have
The maginutde (a scalar or number, it carries the units, too) the direction (in english this means 'in the direction that you measured r') It still carries a magnitude (1), but this is replaced by the other magnitude when they are multiplied (1x something=something).
Another unit vector would be 1 unit east, or 'in the direction I drove'
so you could have 5 km (magnitude) 'in the direction I drove'(unit vector), together they make a normal vector.
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Posted 3 March 2011 - 01:50 AM
It's convenient because you can do math with unit vectors without changing the length of your original vector. For example, in physics we might do:
where is a unit vector pointing in the same direction as . In this equation, would be a vector pointing from one object of mass to another object of mass , and would be the gravitational force between them.
If we don't use a unit vector in the equation, we end up multiplying by a vector of some random length, and we make the gravitational force vector too strong or too weak.
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Posted 3 March 2011 - 10:48 AM
Posted 3 March 2011 - 03:41 PM
Those certainly are not the only notations used, even for three space. You will see to denote the unit vectors along the x, y, and z axes, for the spherical unit vectors, and more generically to denote an arbitrary set of unit vectors. That's just a starter.
And of course i, j, and k only pertain to three space.
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