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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).

Direction cosines:

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?

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