Hey, guys. Let's work this one out together. We're gonna find the magnitude of a resultant vector by adding up these 3 vectors over here. So let's check it out. We've got these 3 vectors, but they all actually start from the same place, the origin, which means we're going to have to connect them tip to tail. Then we're going to find the shortest path from the start of the first to the end of the last one. That's what we always do for vector addition. So let's check it out. We have the a vector that's already drawn from the origin and so all I have to do is just connect the b vector tip to tail.

I've got this b vector here, but if you think about this, this b vector goes 3 to the left and then it goes 5 up. So the one way I can sort of move it over is to start from the end of a and I can just go 3 to the left and then 5 up and then my result in or sorry, the b vector is just going to be right here. So basically, I'm kind of like transplanting it over so that it lines up tip to tail. So this is my b vector and I kinda just erase this because I don't need it anymore.

Now, my c vector is going to be the same thing or it's going to be 5 to the left and 2 down. You're just going to add it now tip to tail from this point over here. So you go 1, 2, 3, 4, 5, and then you go 1, 2, so you're going to end up over here. And so now, this is going to be my c vector added tip to tail. So this is c which means I don't need it anymore. Notice how all these things are also parallel. So this c vector is parallel. These c vectors are parallel. That just means that you drew them in the right way.

So that means now that my resultant vector is going to be the start of the first to the end of the last. It's actually instead of you walking this whole path from a to b to c, it is actually just if you walked in the straight line that connects these two points. So this is my d vector here. Now I just have to figure out the magnitude, so I'm just going to break it down into a triangle, figure out the legs just by counting up the squares. So I've got this triangle over here and then I've got 1, 2, 3, 4, 5, 6 and then 1, 2, 3, 4, 5, 6. So I've got a 6 and 6 triangle.

So now, to calculate the magnitude, you just use the Pythagorean theorem. You don't have to worry about the signs, just plug in the numbers of the boxes, 6 squared plus 6 squared, and you just get 8.5. And if you wanted, if it was meters or something like that, then you would just specify the units. So that's the resultant or that is the magnitude of that resultant. Let me know if you guys have any questions.