Mathematical Prerequisites - Introduction to 3D Game Programming with DirectX 9.0 - page 10

We use the following D3DX function to compute the dot product
between two vectors:
FLOAT D3DXVec3Dot( // Returns the result.
CONST D3DXVECTOR3* pV1, // Left sided operand.
CONST D3DXVECTOR3* pV2 // Right sided operand.

);

D3DXVECTOR3 u(1.0f, -1.0f, 0.0f);
D3DXVECTOR3 v(3.0f, 2.0f, 1.0f);

// 1.0*3.0 + -1.0*2.0 + 0.0*1.0
// = 3.0 + -2.0
float dot = D3DXVec3Dot( &u, &v ); // = 1.0

Cross Products
The second form of multiplication that vector math defines is the cross
product. Unlike the dot product, which evaluates to a scalar, the cross
product evaluates to another vector. Taking the cross product of two
vectors, u and v , yields another vector, p , that is mutually orthogonal to
u and v . By that we mean p is orthogonal to u , and p is orthogonal to v .
The cross product is computed like so:

puv [( uv uv ), ( uv uv ), ( uv uv )]

yz zy zx xz xy yx

In component form:

p ( u v u v )

x y z z y

p ( u v u v )

y z x x z

p ( u v u v )

z x y y x

Figure 7: Cross product. The vector u v=p is orthogonal

to both u and v .

Example : Find j = k i = (0, 0, 1) (1, 0, 0) and verify that j is
orthogonal to both k and i .