What is the formula for finding a unit vector?

The formula for finding a unit vector is obtained by taking a vector and dividing it by its magnitude. A vector can be expressed in the form (a \mathbf{i} + b \mathbf{j} + c \mathbf{k}), where (a), (b), and (c) are the components of the vector along the respective coordinate axes, and ( \mathbf{i} ), ( \mathbf{j} ), and ( \mathbf{k} ) are the unit vectors in the direction of the x, y, and z axes, respectively.

To compute the unit vector, you first calculate the magnitude of the vector, denoted as ( |A| ), which is calculated using the formula:

[ |A| = \sqrt{a^2 + b^2 + c^2} ]

Once the magnitude is determined, the unit vector ( \mathbf{u} ) is obtained by normalizing the original vector:

[ \mathbf{u} = \frac{(a \mathbf{i} + b \mathbf{j} + c \mathbf{k})}{|A|} ]

This operation effectively scales the original vector to have a length (magnitude) of