If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Unit vectors intro

Unit vectors are vectors whose magnitude is exactly 1 unit. They are very useful for different reasons. Specifically, the unit vectors [0,1] and [1,0] can form together any other vector. Created by Sal Khan.

## Want to join the conversation?

• I frequently get mixed up between i and j. Is there any trick for remembering which one is which?
• um i got an idea...lets think that j stands for 'jump' so then you would go up(vertical). Rest you can keep the other vector easily in mind i hope :)
• What are the advantages of using these unit vectors notation?
• It makes it easy to add vectors. They're extensively used in Physics, engineering etc.
• Is there a name for the i and j with the hat on top ?
• I have always just called them "i hat" and "j hat". After consulting with the Wiki, that appears to be the official terminology.
• So basically a unit vector is a vector which has only a unit value, as in, either in the horizontal or vertical dimension (Please correct me if I'm wrong). So what's the significance, or what's the point of learning about unit vectors? I mean, usual vectors are just scaled-up unit vectors. So unit vectors are just used for different representations?
• What is the significance? There are quite a few times we would like to have a unit vector. For instance, I recently made a game on the computer science section of the site. In the game, the player is allowed to shoot bullets. When the player clicks the screen, a bullet is fired from the player in the direction of where the mouse was clicked - but how do I make sure that the bullet travels at the same speed, no matter where I click? The solution is to first construct a unit vector from the position of the player to the point that was clicked, and then scale this unit vector to the desired length (which will be the velocity of the bullet). I used a lot of vectors to make this game. Here is the link:

• Why do we use i and j as unit vectors, not x and y or a and b?
• It is notation. If you used x and y then somebody might think you're talking about a point or a line. These both have position. Vectors have no position, so they are distinguished from lines by i and j.
• So, a unit vector and a unit circle are related in some respect - one has a magnitude of 1, the other has a radius of one, right?
• Yes, all unit vectors will touch the unit circle when placed on the origin.
• What is the difference between unit vectors and basis vectors?
• A unit vector is a vector with length/magnitude 1.
A basis is a set of vectors that span the vector space, and the set of vectors are linearly independent. A basis vector is thus a vector in a basis, and it doesn't need to have length 1.
• I do understand this right now, but how can I stick it in my brain ?
• Four things that can help:
1. Get plenty of sleep before you learn or review (sleep has a strong relationship to ability to learn, think, or concentrate: https://youtu.be/09mb78oiPkA?t=42m18s (<-- this is really interesting).
2. Exercise for at least 10 minutes immediately before you learn or review (aerobic exercise immediately before mental activity has been shown to help with recalling memory and learning new things).
3. Practice the concept 1 day after first learning, then 3 days then a week later (Having gradually extending periods between using a concept helps to move the memory from short term to long term memory (possibly most important factor to make something stick).
4. Problem solve using the concept and if you can give yourself a dopamine reward immediately after successfully using the concept (Learning has been shown to be emphasised when the brain can make a clear correlation between an activity and a reward the body/brain wants).

Sorry for not having great links for each point, but this is what I have come across in my journey so far, and has worked well for me. Everything seems to be backed up with scientific evidence.
• Do you use vector notation in your life?
• It's quite rare that a day passes without giving me an opportunity to frame a problem/question/report in terms of vectors. If you've used a computer (since your post was likely made via a computer, I imagine that you have) you've had a use for vectors. Videos (and even images to a lesser extent ) on your computer would require a prohibitively large amount of resources were it not for vectors. You have linear algebra to thank (among many other contributors) every time you hear Sal's ever-patient disembodied voice.
• is the unit vector 'i' always equal to (1,0) or can it also have an arbitrary value?
• No, the unit vector i always has the value <1,0>. This is to indicate a direction relative to some axis system. Think of i as a way of saying East on a graph using vectors.