Online Test Banks
Score higher
See Online Test Banks
eLearning
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

Finding the Unit Vector of a Vector

Every nonzero vector has a corresponding unit vector, which has the same direction as that vector but a magnitude of 1. To find the unit vector u of the vector

image0.png

you divide that vector by its magnitude as follows:

image1.png

Note that this formula uses scalar multiplication, because the numerator is a vector and the denominator is a scalar.

A scalar is just a fancy word for a real number. The name arises because a scalar scales a vector — that is, it changes the scale of a vector. For example, the real number 2 scales the vector v by a factor of 2 so that 2v is twice as long as v.

As you may guess from its name, the unit vector is a vector.

For example, to find the unit vector u of the vector

image2.png

you first calculate its magnitude |q|:

image3.png

Now use the previous formula to calculate the unit vector:

image4.png

You can check that the magnitude of resulting vector u really is 1 as follows:

image5.png
  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
Advertisement

Inside Dummies.com

Dummies.com Sweepstakes

Win $500. Easy.