13.9: Magnitude and Unit Vectors

The magnitude of a vector is its length. For a vector A = [Ax Ay Az], the magnitude is calculated using the square root of the sum of the squares of the components:

\(|A| = sqrt(Ax^2 + Ay^2 + Az^2)\)

In MATLAB, the norm function calculates this for us.

A = [4 -1 2];
magA = norm(A)

A unit vector is a vector with magnitude 1. It keeps the direction of the original vector but removes the size. To create a unit vector, divide the vector by its magnitude:

unitVec = A / norm(A)
norm(unitVec)

The second command should return 1, or a number very close to 1 because of numerical rounding.

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