Unit vector

Unit vector

In this section, we will learn what is a unit vector, which literally refers to a vector with magnitude of 1 unit. We will practice on calculating a unit vector as well as exploring how this concept relates to the basic unit vectors that are found in vectors represented in rectangular form.

Lessons

Unit Vector = a vector with a magnitude of 1
Given vector v\vec{v}, the unit vector in the direction of vector v\vec{v} is obtained as follows:

u^=vv\hat{u}=\frac{\vec{v}}{||\vec{v}||}
where u^=1||\hat{u}||=1
  • Introduction
    Introduction to Unit Vectors

  • 1.
    Find the unit vector of a=\vec{a}= <6,86,-8>, and verify

  • 2.
    What is a unit vector which has the same direction as b=3i+4j\vec{b}=3i+4j?

  • 3.
    Given v=\vec{v}= <10,310,-3> and w=\vec{w}=<6,8-6,8>,
    a)
    find v+w\vec{v}+\vec{w}

    b)
    find the unit vector of the resultant vector


  • 4.
    Given v=\vec{v}= <5,6-5,6> and w=\vec{w}=<7,47,4>,
    a)
    find vw\vec{v}-\vec{w}

    b)
    find the unit vector of the resultant vector