Implementing a Vector3f class and Vectoroperations

Hello,
I implemented a class that represents a vector in 3d space. It has the three float members x,y,z
Now I am courious wether I should implement some of the Mathematic operations as Methods of this class like:
Vec3f getInverse()
float getlength ()
and others
Or should I rather make a new class with some (static) methods for these operations.
I am concerned of performance and memroy. Because I will have to create thousands of these objects.
This brings me to a general question about understanding memory allocation of classes and objects:
How much memory will be allocated for a single instance of a class? Does each instance of a class store the complete methods and their functionality? Or ist it more like this: There is one space in memory (lets call it <A>) for the class and each new instance of that class only stores the rerence adresses to each method that is stored in <A> ? So the instances only have to store the concrete values of its membervariablesand the adresses.
I hope you understand , what I mean.

Don't worry about memory footprint (in this case, that is), the individual instances of your class doesn't have separate copies of the method implementations.
The getLength() method should certainly be imlemented in your vector class, as it describes the state of a particular vector.
What on earth is the inverse of vector??. A three-dimensional vector space is not a ring.
Regards

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    So use an abstract class when the implementation it can carry outweights the fact that it cannot be multiply inherited That's the gist of it.
    The inheritance relationship where this happens is when the supertype is a general concept of which all potential subtypes are special cases. This is called a specialization (or sometimes a generalization) relationship. For example Apple and Banana are Fruit. Or Car and Bike are Vechicle. The Fruit and Vechicle supertypes are general concepts of which their subtypes are special cases. In this case make Fruit and Vechicle abstract classes because the subtypes will benefit from a shared implementation.
    If you don't have a clearcut specialization/generalization relationship make the supertype an interface. An example could be the Comparable supertype. The potential subtypes aren't supposed to be specializations of the Comparable concept, they're suppose to become Comparable (and make this property an integral part of their being). This is not a specialization/generalization relationship. Instead the supertype is intended to add character to the subtypes. The subtypes are unlikely to benefit from an inherited implementation. So make Comparable an interface.

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