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# Unit vector notation

Learn how to factor in magnitude and direction when adding and subtracting vectors. See how to break vectors into x and y components, and how to use unit vector notation to label vectors in a way that represents them more efficiently and analytically, making it easier to add and subtract them. Created by Sal Khan.

## Want to join the conversation?

• So the unit vector notation is the same as engineering notation for vectors?
• Yes,but this similarity is in their conceptualizations:
-Engineering Notation is the representation of a ''vector'' by its individual components.
-And as such by definition Unit vector notation is the analytically representation of 2 dimensional vector - in that, any 2-D vector can be represented by any combination of these U.Vectors
One could then say that they fall in the same category.
• what's the answer to this question ?

-> a = i^ + j^ - K^, b = i^ - j^- k^
Find = a-b

P.S.- can't properly write i cap, j cap, k cap. I hope you understand!
• it would be 2j^
• If you added a i vector and a j vector what would it equal?
• It will be i + j
• How is I and j vector are practically used in our life (like spacecraft moving or launched with help of vector calculations)
• So V=5sqrt3i + 5j. But in the question it is given that V=10. And, 5sqrt3 + 5 is not equal to 10. Can somebody please explain?
• I think what you're missing (it isn't well explained) is that unit vector notation is an alternate way to define a vector, not an actual equation. The i-hat, j-hat, k-hat etc don't just disappear and allow you to add the values to get the magnitude of v. You need to forget about the plus or minus sign as an operator in this and think of it as an indicator of positive or negative values. To visualize what I'm saying, try using a comma in the unit vector notation: (+5) i hat, (-3) j hat. The plus and minus are not operators when you use a comma and parentheses like this, and that is where you need to bring your brain. It is a shorthand way of writing out the individual components of a vector, which becomes very useful when manipulating multiple vectors. Add a vector with a magnitude 10 at 30 degrees to a vector of magnitude 5 at 90 degrees. Since you already need to break the vectors into components to solve the problem, 5sqrt3 ihat+5 jhat, and 0 ihat+5jhat, you can present the vector as 5sqrt3 ihat+10 jhat. this is simpler to work with than the magnitude degree calculation of magnitude is sqrt(5sqrt3^2+10^) and direction is arctan 10/5sqrt3. Both define the same vector, the vector notation is simply cleaner and more easily worked with.
• So if sum two vectors we join them head to tail? and what if i wanna subtract them (visually/in a diagram or something)?
• To subtract or add them we use the tail to tip method where we put the head of one on the tail of another. The reason for this is that there are no negative vectors or lines, they just go in different directions. Simply, there is no subtraction or negatives.
• So how do you know weather to use sine or cosine when dealing with Vx and Vy??
• you need to draw your triangle and figure out whether the side you are trying to figure out is opposite or adjacent. If it's opposite, you are going to use sine. Adjacent will be cosine.
• Why does Sal tend to use an angle off of the x-axis when talking vectors as opposed to the more conventional y-axis?
• In physics the convention is to use the x-axis, probably because it's easier to measure the angle from the horizontal in real life (the x-axis would be the ground, or the top of a table, or whatever) than to measure the angle from the vertical (which would be straight upward and more difficult to find a line to measure against). I've seen the y-axis convention more in trig, usually in navigation-related applications in which the y-axis represents north.
• can someone clear my doubt?
imagine i have 3 points in xyz space.. and those points are collinear.......
if the vector positions of those 3 points have different direction.... would those vector's would be termed as collinear? since those points are collinear??