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

Lesson 4: Vector addition & subtraction

# Adding & subtracting vectors end-to-end

Build intuition behind adding and subtracting vectors visually and the "end-to-end" method.

## Want to join the conversation?

• At last in the video Sal said that vector a + vector b= -vector c , then it can be also written as vector a + vector b + vector c = 0 , but here will it be scalar 0 or vector 0 ?
• If I am given a triangle whose 2 sides are denoted by vector a and vector b, what would the third side?
Should it be( a+b) Or( a-b) ?
• It depends on how the vectors are oriented.

If, for example, 𝒂 and 𝒃 originate from the same point, and 𝒄 goes from the endpoint of 𝒃 to the endpoint of 𝒂, then 𝒄 = 𝒂 − 𝒃.

But, if 𝒃 starts at the endpoint of 𝒂, and 𝒄 goes from the starting point of 𝒂 to the endpoint of 𝒃, then 𝒄 = 𝒂 + 𝒃.

In total there are 8 different constellations, and depending on which one it is 𝒄 can be either 𝒂 + 𝒃, 𝒂 − 𝒃, 𝒃 − 𝒂, or −𝒂 − 𝒃
• what if vector a and b are perpendicular? would we use pythagoras' theorem or vector addition?
• If we are trying to find the distance from the starting point to the end point, then we would use the Pythagorean theorem. In other words, if we are trying to find the magnitude of the vector, we would use the Pythagorean theorem.

If we are trying to find the displacement, then we would use vector addition.
• Can we draw a scalar? My math teacher says that we can't draw a scalar, but I think that the side of a triangle, for example is a scalar.
• Basing my answer off of what my physics teacher had said, distance --the shortest path from one point to another -- is a scalar. You can draw this path with a straight line segment. So, I would argue that you can draw a scalar as a line segment.
• does that mean that the magnitude of a vector is the sum of two vectors?
• No, a vector can be said to be the sum of one or more component vectors, but the magnitude of the vector is equal to sqrt((x^2) + (y^2)) where x and y are the component vectors. (This can also be extended to calculate the magnitude of vectors in more than 2 dimensions.)
• i think he showed wrong direction of resultant vector c it should be from tail of a to head of b which is shown wrong i think
• You might want to listen more closely to what Sal was saying. In the second example he was working, the vector C he was using was NOT the sum of vectors A and B. Once he switched directions as you suggest to create the vector -C he then set up the equation A + B = -C.
• Why do we take -c instead of +c?
• It has to do with c's starting point. In the first problem, A+B=C, The terminal end of A,(the end with the arrow) is the initial end of B. C shared a starting point with A and a terminal point with B.
Now look at how he drew it for A -B = D, and you should start to get it. I recommend that you see if you can figure out why the direction matters. Its good exercise for the brain.
• At , Sal says it's going in a circle. Isn't it going in a triangle?
(1 vote)
• Yes, I think he is just saying "circle" to show that it's going "around" and you will eventually end up where you started, able to repeat the cycle again.