Creating Unit Vectors: How to Normalize a Given Vector for Same Direction

Find unit vector (u) with the same direction

To find a unit vector with the same direction as a given vector, we need to normalize the given vector

To find a unit vector with the same direction as a given vector, we need to normalize the given vector.

Let’s assume the given vector is V = (v1, v2, v3).

Step 1: Calculate the magnitude (length) of the vector V.

The magnitude of a vector V = √(v1^2 + v2^2 + v3^2)

Step 2: Divide each component of the vector V by its magnitude.

v1_normalized = v1 / |V|
v2_normalized = v2 / |V|
v3_normalized = v3 / |V|

Step 3: Combine the normalized components to form the unit vector u.

u = (v1_normalized, v2_normalized, v3_normalized)

The resulting vector u will have the same direction as the original vector V but will have a length/magnitude of 1, making it a unit vector.

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