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### Course: Algebra (all content)>Unit 19

Lesson 6: Unit vectors

# Worked example: finding unit vector with given direction

Learn what a unit vector is and how to find a unit vector in the direction of a given vector. Created by Sal Khan.

## Want to join the conversation?

• As Sal Sir said that a unit vector has magnitude one , can it has magnitude -1?
• Magnitude is the length of something. If you had a ruler and measured it, that would be the magnitude. Lengths cannot be negative, so they must always be positive.
• What is the use of using unit vector ? why do we Consider unit vector for any vector ?
• A unit vector contains directional information. If you multiply a positive scalar by a unit vector, then you produce a vector with magnitude equal to that scalar in the direction of the unit vector.
• What is the significance of finding a unit vector? What does it allow you to do? I'm in an engineering course
• Did you ever see the movie Despicable Me 1? Remember the character Vector, who has both "Magnitude" and "Direction".
Well this is precisely what a vector is, a mathematical object with magnitude and direction.
When we talk about a unit vector, we are talking about a vector whose magnitude is 1 in a given direction. Sometimes you may here the unit vector called a direction vector, because all it really does is tell you what direction the object is going in.
Once we have the unit vector, or direction, we can multiply it by the magnitude to describe the properties of the object with that particular vector, that is, with that particular magnitude and direction. This is VERY HANDY
Try this: https://www.mathsisfun.com/algebra/vector-unit.html
and this: https://en.wikipedia.org/wiki/Unit_vector
• The unit vector in this example ends up being the cos and sin of the angle formed by the original vector and the x-axis. Will this always be the case? If it is, how useful is this?
• That will always be the case, much of trigonometry is based around this relationship.
• At 3: 08, (When he made a unit vector U,) why did he divide 3 and 4 by the magnitude of vector A?
• Because a unit vector, by definition, has a magnitude of 1, so if you want a unit vector in the direction of A you need to divide by its magnitude.
• In earlier videos when Sal used the hat with i and j e.g. 7i^ + 8j^ does that just mean 7+8 because the hat is just 1 unit?

Thanks
• i^ is usually defined as a unit vector that goes along positive x-axis for one unit, while j^ is usually used to denote a unit vector that goes along positive y-axis for one unit. So, 7i^ + 8j^ is representing a vector that goes 7 units to the right in the horizontal direction and 8 units up in the vertical direction from its initial point to its terminal point. Since i^ and j^ represent different vectors from the first place, we can't just add their coefficients.
• In the last video "Unit vectors intro", Sal uses `i^ = (1, 0)` and `j^ = (0, 1)` to make `vector v = 2i^ + 3j^` (and `vector v = (2,3)`). As the unit vector taught in this video has the denominator to be ||vector||, why wasn't `vector v = (2/sqrt(13), 3/sqrt(13))` instead?
• Sal never claims that v is a unit vector. The unit vectors he introduces are just î and j-hat.
• Can the magnitude be a negative number?
• no since +ve or -ve signs only indicate direction.