Imagine a triangle with all the sides of different length. If you walk around it, you still end up in the same place.
Take each side of this triangle to be a vector with length of the side and direction of your movement. Each vector starts at the end of previous one, which is how we add vectors - they don't even have to start at the end of each other actually, because for every set of vectors it can be easily arranged.
Since you end up in the same place where you started, the total displacement is zero and so the sum of unequal vectors can be zero.