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
Inspiration Through Photography | National Geographic
These quests are a challenge for these photographers, but they’re also a way to help them frame their experience. All three of them bring something unique; I think that’s what’s so rewarding about these assignments. They were put to the test. People surro…
The Incredible Sounds of the Falcon Heavy Launch (BINAURAL AUDIO IMMERSION) - Smarter Every Day 189
Hey, it’s me, Destin. Welcome back to Smarter Every Day. So, the SpaceX Falcon Heavy test flight just happened; everyone agrees the footage is phenomenal. It was amazing technological wizardry. Everyone loves it, but there’s something that is missing whe…
Angular momentum of an extended object | Physics | Khan Academy
[Voiceover] So we saw in previous videos that a ball of mass m rotating in a circle of radius r at a speed v has what we call angular momentum, and the symbol we use for angular momentum is a capital L. The amount of angular momentum that it would have wo…
How to Destroy a $100 Billion Valuation
Shiin is an incredibly successful Chinese fast fashion company known for making unbelievably inexpensive apparel that’s insanely popular with Gen ZZ consumers. It was one of these companies that absolutely flourished during COVID times. They are an early …
Geoengineering: A Horrible Idea We Might Have to Do
By the end of the 21st century, humanity is becoming desperate. Decades of heat waves and droughts have led to unusually poor harvests, while the warming oceans yield fewer fish each year in the tropical zones. Millions suffer from famines, and resource w…
Health insurance primer
What we’re going to do in this video is try to break down the terminology and a little bit of the math of health insurance. So the first question that you might wonder is: how much does an insurance plan cost? In many cases, you might have an employer who…