Home All Definitions Pre-Calculus Unit Vector Definition

Unit Vector Definition

A unit vector is a vector with a length or magnitude of 1. Sometimes, the unit vector is also called a direction vector. Often a unit vector is written using the ⃗ symbol above. For instance, u⃗ is a unit vector pointing in the same direction as the vector u.

The unit vector v⃗ having the same direction as a given (nonzero) vector v is defined by v⃗ = v|v|, where |v| denotes the norm of v, is the unit vector in the same direction as the (finite) vector v. A unit vector in the xn direction is given by x⃗n = r∂xnr∂xn, where r is the radius vector. When considered as the ith basis vector of a vector space, a unit vector may be written ei (or e⃗i).

Related Definitions

Sources

“Unit Vector.” From Wolfram MathWorld, mathworld.wolfram.com/UnitVector.html.

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