Sefine the points \( P(-9,5) \) and \( Q(-3,9) \). Carry out the following calculation. Express \( \overrightarrow{P Q} \) in the form \( a \mathbf{i}+\mathrm{bj} \). \( \overrightarrow{P Q}=(\square) \mathbf{i}+(\square) \mathbf{j} \) (Simplify your answers.)

To find the vector \( \overrightarrow{PQ} \) in the form \( a\mathbf{i} + b\mathbf{j} \), follow these steps: 1. **Identify the coordinates of points \( P \) and \( Q \):** - \( P(-9, 5) \) - \( Q(-3, 9) \) 2. **Calculate the difference in the \( x \)-coordinates and the \( y \)-coordinates:** - Difference in \( x \)-coordinates: \( x_Q - x_P = -3 - (-9) = 6 \) - Difference in \( y \)-coordinates: \( y_Q - y_P = 9 - 5 = 4 \) 3. **Express the vector \( \overrightarrow{PQ} \) using the differences:** \[ \overrightarrow{PQ} = 6\mathbf{i} + 4\mathbf{j} \] **Final Answer:** \[ \overrightarrow{PQ} = 6\,\mathbf{i} + 4\,\mathbf{j} \]