The problem you shared consists of two main tasks. Let's focus on the second part:

Part 2:

You are asked to find the following vector magnitudes and distances between points:

1. Find vector $\overrightarrow{AB}$

   • Use the formula for finding the vector from point $A(x_1, y_1)$ to point $B(x_2, y_2)$: $\overrightarrow{AB} = (x_2 - x_1, y_2 - y_1)$ Substituting the coordinates of $A(5, 1)$ and $B(-2, 5)$, we get: $\overrightarrow{AB} = (-2 - 5, 5 - 1) = (-7, 4)$

2. Find vector $\overrightarrow{AC}$

   • Similarly, use the formula for vector $\overrightarrow{AC}$ with points $A(5, 1)$ and $C(6, 0)$: $\overrightarrow{AC} = (6 - 5, 0 - 1) = (1, -1)$

3. Find vector $\overrightarrow{BA}$

   • The vector $\overrightarrow{BA}$ is the reverse of $\overrightarrow{AB}$: $\overrightarrow{BA} = (5 - (-2), 1 - 5) = (7, -4)$

4. Find vector $\overrightarrow{ABC}$

   • To find $\overrightarrow{ABC}$, we need the direction of vector $\overrightarrow{AB}$ followed by vector $\overrightarrow{BC}$. First, calculate vector $\overrightarrow{BC}$ with points $B(-2, 5)$ and $C(6, 0)$: $\overrightarrow{BC} = (6 - (-2), 0 - 5) = (8, -5)$ Then, the vector $\overrightarrow{ABC}$ is $\overrightarrow{AB} + \overrightarrow{BC}$: $\overrightarrow{ABC} = (-7 + 8, 4 - 5) = (1, -1)$

Let me know if you'd like further clarification or if you'd like to proceed to the calculations of the lengths and magnitudes.