Find the magnitude of the vector sum $\vec{A}+\vec{B}+\vec{C}$. Each grid square is $200 \mathrm{~N}$ on a side. If the vector sum is to the west, enter a negative value. If the vector sum is to the east, enter a positive value. $\mathrm{N}$

Step 1 ：Find the components of each vector:

Step 2 ：Vector A: x-component = 0, y-component = 3 squares * 200 N/square = \(600 N\)

Step 3 ：Vector B: x-component = -2 squares * 200 N/square = \(-400 N\), y-component = 0

Step 4 ：Vector C: x-component = 1 square * 200 N/square = \(200 N\), y-component = -1 square * 200 N/square = \(-200 N\)

Step 5 ：Add the components of each vector to find the vector sum:

Step 6 ：Vector Sum: x-component = 0 + (-400) + 200 = \(-200 N\), y-component = 600 + 0 + (-200) = \(400 N\)

Step 7 ：Find the magnitude of the vector sum:

Step 8 ：\(\sqrt{(-200)^2 + (400)^2} \approx 447.21 N\)

Step 9 ：\(\boxed{447.21 N}\)