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Algebra (all content)

Course: Algebra (all content)>Unit 19

Lesson 4: Vector addition & subtraction

Sal shows how to add vectors by adding their components, then explains the intuition behind adding vectors using a graph.

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• Why do vectors "combine" to form new vectors like that?
• The intuition behind this "combination" is that the resultant vector of ,say, 2 vectors would be the addition of those vectors.
Example : If the displacement of a person is 5 miles east ,and then 2 miles south ,their resultant displacement vector would be the sum of the 2 previous vectors.
• Don't we put the X and Y values in a matrix sort of form? Where the X is above and the Y below?
• I think you are referring to the vector multiplication. Here Sal is talking about addition and subtraction.
• I am stuck on the following:

eg. u (-6, -6) w (-8, -7)
u-w = (-6 (-8), -6 (-7))

I dont know to graphically represent this! any help?
• Instead of thinking it as subtracting w think of it as adding negative w. So negative w is like scaling w by -1 which you probably learnt in one of the previous videos. This makes (-8*-1,-7*-1)=(8,7). So take the vector u and add the vector -w to u. the way to graph it is just graph u from the origin and then graph -w by placing the initial point at the terminal point of u and drawing a line from the initial point of u which is the origin to the terminal point of -w which would be at (2,1). So when subtracting the two vectors, the new vector is equal to a x component of 2 and a y component of 1.
• When adding vectors, do you have to always write it out like how he did it in the video, or could you just be a little quicker and do it in your head? Is there a difference?
• if you are just doing a calculation that you are comfortable with, it makes little sense to write it out, when you can just do it in your head. But if you are not completely adept at the skill, you will make mistakes occasionally, and writing it down lets you check your process to see where/how/why the mistake was made.

You dont learn from doing calculations in your head, you learn from making mistakes, and then figuring out why.
• Hey when do add and subtract vectors? like in what scenarios would you add the vectors or subtract them?
• You would add and subtract vectors if you were trying to plot the direct route to a certain point. Say, Bob went north 9 meters and then went East for 12 meters. 9m @ 90° + 12m @ 0° = 15m @ 36.87°
So you could go 15m at a 36.87° angle to get to Bob "as the Crow flies."
• and why do we also use matrices for vectors operations ?
• Vectors can be seen as nx1 matrices, So vector operations are basically an extension of matrix operations
• I don't understand what Sal means when he says that these vectors are 2 Dimensional (I'm pretty sure he mentioned this in another video). What does 2D mean in this circumstance? What would 3D look like?

• Another way to think about it is the number of ways that a shape can move. A 3D shape can move up/down, left/right, and backwards/forwards (3 ways). A 2D shape can move up/down and left/right (2 ways). A 1D shape can move left/right (1 way). And a 0D shape cannot move at all. The only thing to remember with this way is that a dimension is not restricted to one direction of movement, so a shape that can move in/out (however that works) is in the 1D just as much as a shape that can move left/right.
• At , Sal says '2-dimensional vectors'.
Do 3-dimensional vectors exist?