If v is a three dimensional vector, then |v| represents the length of v. |v| is defined as follows:
|v| = √x² + y² + z²
We will use two points in three dimensional space, (a,b,c) and (d,e,f), to further clarify the definitions of x, y, and z in this context.
x = (d – a), y = (e – b), z = (f – c).
cos θ₀ = x/|v|, cos θ₁ = y/|v|, cos θ₂ = z/|v|.
Theta, in this context, is sometimes referred to as a direction angle.
If the smallest nonnegative value of the three angles represents the direction of the vector v, what is the significance of the direction cosines?