Mathematical Prerequisites - Introduction to 3D Game Programming with DirectX 9.0 - page 7

FLOAT D3DXVec3Length( // Returns the magnitude.
CONST D3DXVECTOR3* pV // The vector to compute the length of.

);

D3DXVECTOR3 v(1.0f, 2.0f, 3.0f);
float magnitude = D3DXVec3Length( &v ); // = sqrt(14)

Normalizing a Vector
Normalizing a vector makes a vector's magnitude equal to one, which is
called a unit vector. We can normalize a vector by dividing each compo-
nent by the vector's magnitude, as shown here:

u

u uuuu u u

ˆ

y

x

, ,

z

We denote a unit vector by putting a hat over it: û .
Example : Normalize the vectors u = (1, 2, 3) and v = (1, 1).
Solution: From equations (2) and (3) we have u 14 and v 2, so:

u 1 2 3

ˆ

u , ,

14 14 14 14

v 1 1

ˆ

v ,

2 2 2

Using the D3DX library, we can normalize a vector using the following
function:
D3DXVECTOR3 *D3DXVec3Normalize(
D3DXVECTOR3* pOut, // Result.
CONST D3DXVECTOR3* pV // The vector to normalize.

);

Note: This function returns a pointer to the result so that it can be
passed as a parameter to another function. For the most part, unless
otherwise stated, a D3DX math function returns a pointer to the result.
We will not explicitly say this for every function.

Vector Addition
We can add two vectors by adding their corresponding components
together; note that the vectors being added must be of the same
dimension:

uv ( uvuvuv , , )

x x y y z z