1. ## Vector class

Hey there. I'm pursuing my Matrix class and would like to make it work together with a Vector class I'm developing as well. I have a design question however and a technical question as well.

First, here's the code for the Vector class right now:
Code:
```#ifndef VECTOR_H_INCLUDED
#define VECTOR_H_INCLUDED

#include <vector>

template < class T >
class Vector
{
public:
Vector(int n = 3);
Vector(const Vector< T >&);

// Not quite sure about the type it should return...
float Angle( ) const;
void Normalize( );
float Length( ) const;

Vector< T > VecProduct(const Vector< T >&) const;
T DotProduct(const Vector< T >&) const;

bool IsParallel(const Vector< T >&) const;
bool IsOrthogonal(const Vector< T >&) const;

bool operator == (const Vector< T >&) const;
bool operator != (const Vector< T >&) const;
Vector< T >& operator = (const Vector< T >&);
Vector< T >& operator += (const Vector< T >&);
Vector< T >& operator + (const Vector< T >&) const;
Vector< T >& operator -= (const Vector< T >&);
Vector< T >& operator - (const Vector< T >&) const;
Vector< T >& operator *= (const T&);
Vector< T >& operator * (const T&) const;

private:

};

#endif // VECTOR_H_INCLUDED```
It isn't as complete as it should, but this is a good start for a beginner's Vector class. I want to be able to use that Vector class with matrices; therefore I need it to let the user use a 2, 3, 5 or even 10 dimension vector. I first thought about using std::auto_ptr< > and allocate enough memory for each dimension, but copying objects would be a mess because of pointer ownership. Then I thought of using a vector, but it seems like overhead to me since vectors don't usually get large enough for vectors to be efficient. I thought then to use a pointer and allocate memory dynamically but this seems a bit hack-ish to me. Do you guys know a good way to solve that problem ?

Also, the technical question is rather simple, in fact. What type should the Angle() function return ? I thought returning a T would be dangerous because if T happens to be 'int' then we lose precision (which is also a problem for Normalize() and Length()). Then I thought returning float would be correct because of its precision but I'm not 100&#37; sure.

Thanks a lot.

2. You have a choice in the second option - do you want to return degrees or radians? Either way I'd return a double of some description - I never liked the float type much. Make a method for each option. You might also want to consider returning a COORD, x and y values. There's no point in just working in polar coordinates. The other one, that I can say but not spell, is useful too. For the former question ... could be difficult to have the number of dimensions as a variable. Stick with fixing a static number of dimensions first.

3. In general, an std::vector is as efficient as any other similar dynamic memory solution. Since the size of your Vector will be dynamic, you will probably want to use dynamic memory. So, I would use std::vector. If you want to cap the size of your Vector at something small like 10, then a local array of that maximum might be an option to avoid dynamic allocation.