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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?

Linear algebra resources from Amazon.com

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