# Video: Adding Components of Two Vectors in 2D

𝑎 = 〈3, 2〉, 𝑏 = 〈4, −1〉, find 𝑎 + 𝑏.

01:43

### Video Transcript

We’ve got 𝑎 which is the vector three, two and 𝑏 which is the vector four, negative one. And we want to add those two vectors together. So just quickly sketching those out, here we’ve got vector 𝑎 which has an 𝑥-component of positive three and a 𝑦-component of positive two — so we’ve gone three in that direction, two in that direction — and 𝑏, which has an 𝑥-component of four and a 𝑦-component of negative one.

So if we add these two vectors, it’s like laying them end to end and then working out how we get from the beginning of the first vector to the end of the last vector. So to get from here to here, we’ve taken a journey of three in the 𝑥-direction here and another four in the 𝑥-direction here. So to find the 𝑥-component of the resultant vector, 𝑎 plus 𝑏, we simply add the 𝑥-component of 𝑎 to the 𝑥-component of 𝑏.

And now let’s visit the 𝑦-components. So to get from here to here again, we’ve done our positive two to take us up to the top of the diagram but then we came back one. So we’ve got to add those two components together. So that’s two plus negative one. And three and four makes seven, so the resultant 𝑥-component is seven. And two add negative one is one, so the resultant 𝑦-component is one.