Answers.Body: <p>Given the <a href="https://en.wikipedia.org/wiki/Axis%E2%80%93angle_representation" rel="nofollow noreferrer">axis-angle</a> rotation vector <span class="math-container">$\Theta = (2, 2, 0)$</span>, you can find the unit vector in the same direction by diving by the norm (or length) of <span class="math-container">$\Theta$</span>, denoted by <span class="math-container">$\|\Theta\| = \sqrt{2^2 + 2^2 + 0^2} = \sqrt{8} = 2\sqrt{2}$</span>. Therefore, the unit vector in the direction of <span class="math-container">$\Theta$</span> is <span class="math-container">$k= \Theta/\|\Theta\| = (1/\sqrt{2}, 1/\sqrt{2}, 0)$</span>, which should be the axis of rotation that you're looking for. The angle should just be the norm of <span class="math-container">$\Theta$</span>, that is, <span class="math-container">$\theta = \|\Theta\| = 2\sqrt{2}$</span>. Note that <span class="math-container">$k \theta$</span> gives you your original vector <span class="math-container">$\Theta$</span>.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2019-08-18T17:12:30.590Z
Answers.LastActivityDate: 2019-08-18T17:23:39.153Z
Answers.LastEditDate: 2019-08-18T17:23:39.153Z
Answers.UserDisplayName: nbro
Body: <p>I have a robotics assignment, which I am unable to solve. Given the axis-angle rotation vector <span class="math-container">$\Theta = (2, 2, 0)$</span>, how can I calculate the unit vector of the rotation axis <span class="math-container">$k$</span> and the angle <span class="math-container">$\theta$</span>?</p>
  
Tags: <math><robotics><homework>
Title: Given an axis-angle rotation vector, how can I find the unit rotation axis and angle?
UserDisplayName: Qebap
ThreadText: # Given an axis-angle rotation vector, how can I find the unit rotation axis and angle?
  
  (Asked by: username_0 on 2019-08-18)
  
  I have a robotics assignment, which I am unable to solve. Given the axis-angle rotation vector $\Theta = (2, 2, 0)$, how can I calculate the unit vector of the rotation axis $k$ and the angle $\theta$?
  
  **Tags:** math, robotics, homework
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2019-08-18. Score: 0
  
  Given the [axis-angle](https://en.wikipedia.org/wiki/Axis%E2%80%93angle_representation) rotation vector $\Theta = (2, 2, 0)$, you can find the unit vector in the same direction by diving by the norm (or length) of $\Theta$, denoted by $\|\Theta\| = \sqrt{2^2 + 2^2 + 0^2} = \sqrt{8} = 2\sqrt{2}$. Therefore, the unit vector in the direction of $\Theta$ is $k= \Theta/\|\Theta\| = (1/\sqrt{2}, 1/\sqrt{2}, 0)$, which should be the axis of rotation that you're looking for. The angle should just be the norm of $\Theta$, that is, $\theta = \|\Theta\| = 2\sqrt{2}$. Note that $k \theta$ gives you your original vector $\Theta$.
  
  
  ---
  
  