A simple sequence processing model generates an output vector, $y_i$, for each input vector, $x_i$, in a sequence. The output $y_i$ is a weighted sum of all input vectors up to and including $x_i$. The weights are determined by a three-step process:

1. Scoring: A score is calculated between the current input $x_i$ and each preceding input $x_j$ (where $j \le i$) using a dot product: $score(x_i, x_j) = x_i \cdot x_j$.
2. Normalization: These scores are converted into weights, $\alpha_{ij}$, by applying a softmax function across all $j \le i$.
3. Output Calculation: The output $y_i$ is calculated as the weighted sum: $y_i = \sum_{j \le i} \alpha_{ij} x_j$.

Your task is to apply this process to calculate the final output vector, $y_3$, for the given sequence.