Good job! Be careful when working with vectors that are not of the same size as you will get **unexpected results**.

When you try to sum two vectors of different lengths, R responds by **stretching the smaller vector** so it matches the length of the **longer vector**. It does this by recycling each element **from the start** of the smaller vector, one by one, and **appending them** to its end. For example, suppose we try to sum the following two vectors:

c(1, 2, 3, 4, 5) + c(10, 20)

Under the hood, R will treat the second vector as `c(10, 20, 10, 20, 10)`

. The result of adding the two vectors will thus be:

[1] 11 22 13 24 15

Note that this is also how operations with single-value vectors work.

In other words, when we add a **single value** to a vector, such as

c(1, 2, 3, 4, 5) + 5

R takes the single element (which in reality is treated as a vector) and recycles its elements (in this case, there's only one element) until it matches the length of the other vector.