yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Parallelogram rule for vector addition | Vectors | Precalculus | Khan Academy


2m read
·Nov 10, 2024

  • [Instructor] So we have two vectors here, vector A and vector B. And what we're gonna do in this video is think about what it means to add vectors. So, for example, how could we think about what does it mean to take vector A and add to that vector B? And as we'll see, we'll get another third vector.

And there's two ways that we can think about this visually. One way is to say, all right, if we want to start with vector A and then add vector B to it, what we can do is take a copy of vector B and put its tail right at the head of vector A. Notice I have not changed the magnitude or the direction of vector B. If I did, I would actually be changing the vector.

And when I do it like that, this defines a third vector which we can use as the sum of A plus B. The sum is going to start at the tail of vector A and end at the head of vector B here. So, let me draw that. It would look something like that. And we can call this right over here, vector C. So we could say A plus B is equal to vector C.

Now we could have also thought about it the other way around. We could have said, let's start with vector B and then add vector A to that. So I'll start with the tail of vector B and then at the head of vector B, I'm going to put the tail of vector A. So it could look something like that.

And then once again, the sum is going to have its tail at our starting point here and its head at our finishing point. Now, another way of thinking about it is we've just constructed a parallelogram with these two vectors by putting both of their tails together. By taking a copy of each of them and putting that copy's tail at the head of the other vector, you construct a parallelogram like this, and then the sum is going to be the diagonal of the parallelogram.

But hopefully you appreciate this is the same exact idea. If you just add by putting the head to tail of the two vectors and you construct a triangle, the parallelogram just helps us appreciate that you can start with the yellow vector and then the blue vector or the blue vector first and then the yellow vector. But either way, the sum is going to be this vector C.

More Articles

View All
Benefits explained | Employment | Financial Literacy | Khan Academy
Hi everyone! So, what I’m going to do in this video is really go through a bunch of terms that you’re going to see when thinking about benefits from your employer. The whole goal here is so that you’re never lost when you hear an acronym like 401k—well, t…
Tiger Shark Database | World's Biggest Tiger Shark?
NARRATOR: Next day, back in the Polynesian town of Papetoai, they visit an expert who ID sharks by their fins. So we were hoping to see if you could look through some of your databases. NARRATOR: Shark scientist Nicolas Buray keeps a photo archive of Tah…
How the algorithm controls your life
One thing that I’m really starting to notice is that it’s becoming extremely difficult not to spend all of our time on social media, on the internet, and all of that during these times of isolation. As if it wasn’t already a huge problem. And it kind of m…
Impact of removing outliers on regression lines | AP Statistics | Khan Academy
The scatter plot below displays a set of bivariate data along with its least squares regression line. Consider removing the outlier at (95, 1). So, (95, 1) we’re talking about that outlier right over there and calculating a new least squares regression li…
Example finding critical t value
We are asked what is the critical value t star (t asterix) for constructing a 98% confidence interval for the mean from a sample size of n, which is equal to 15 observations. So just as a reminder of what’s going on here, you have some population. There’…
Ask me anything with Sal Khan: May 15 | Homeroom with Sal
Hi everyone, welcome to the daily homeroom livestream. For those of you all who are wondering what this is, when we started having physical school closures, we realized—and everyone had to be socially distant—we realized that it’s our duty really, as a no…