This question is from Gilbert Strang's "An introduction to Linear Algebra (5)" - section 1.1 question 14.
The picture below is a twelve clock vector. The question is broken down into several parts. The first part asks for the sum of vectors if one starts from the middle of the clock (pos (0,0)) - the answer to which is the zero-vector.
The fourth part is this: Suppose the twelve vectors start from 6:00 at the bottom instead of (0,0) at the center. The vector to 12:00 is doubled to (0,2). Add the twelve new vectors.
What is the sum of the twelve vectors?
Addition to address the hold: I don't understand why the prompt includes the information: "The vector to 12:00 is doubled to (0,2)." Does this imply that the location of 6:00 is (0,1)? I'm also not sure what the significance of the clock form is. Would we lose the clock shape when moving the starting point to 6:00?
The twelve original vectors add up to the zero vector, i.e. $v_1 +\cdots+v_{12}=\mathbf{0}$.
Each of the new vectors is obtained by adding $(0,1)$ to each of the old vectors. Adding everything up gives $(v_1+(0,1)) + \cdots + (v_{12}+(0,1)) = (0,12)$.