# Euclidean distance from zero

I am trying to create my own weights for relative work task importance, or weight. For every task, I have a value of importance, frequency, and relevance. I was recommended to use Euclidean distance from zero to create the weight per task. However, I can't seem to find anything on the internet, why to use such measure at all, and also why it would be better than simply the average of all three.

Is there any specific term for "Euclidean distance from zero" so that I can dig into the pros and cons?

• "Euclidean distance from zero" is just the length of a vector $\begin{bmatrix} importance_i\\frecuency_i\\relevance_i\end{bmatrix}$, for some task $i$, where each axis corresponds to one feature of a task. – Mentossinho Jul 23 '20 at 19:07
• Thanks @Mentossinho. So, this is different from the difference between the three data points. Would you have some reading material (web pages or so) that you recommend me to read about it? – Marc Jul 23 '20 at 19:30
• Also, is this Euclidean length, and if so, is that the same as Euclidean norm? – Marc Jul 23 '20 at 19:37
• Yes, this is exactly the Euclidean norm. The difference between two data points $i$ and $j$ looks like: $\sqrt{(importance_i-importance_j)^2+(frequcency_i-frequency_j)^2+(relevance_i-relevance_j)^2}$ and this is an Euclidean metric induced by a norm mentioned above. I haven't any particular source to learn, maybe this aricle from wiki could be helpful: en.wikipedia.org/wiki/Euclidean_distance. – Mentossinho Jul 23 '20 at 19:50
• Thank you so much @Mentossinho!! I can not accept your answer unfortunately – Marc Jul 23 '20 at 22:11