To find the magnitude of the vector $\overrightarrow{AB}$, we use the distance formula. The formula for the magnitude of a vector between two points $A(x_1, y_1)$ and $B(x_2, y_2)$ is:

$|AB| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Given:

• $A(6, 12)$
• $B(-3, -4)$

Substitute the coordinates into the formula:

$|AB| = \sqrt{(-3 - 6)^2 + (-4 - 12)^2}$ $|AB| = \sqrt{(-9)^2 + (-16)^2}$ $|AB| = \sqrt{81 + 256}$ $|AB| = \sqrt{337}$

Thus, the magnitude of $\overrightarrow{AB}$ is:

$|AB| = \sqrt{337} \approx 18.3576$

If you'd like further details on the process or have any other questions, feel free to ask!

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Here are 5 related questions you might find helpful:

1. How do you calculate the distance between two points in 3D space?
2. What is the dot product of two vectors, and how is it related to the magnitude of vectors?
3. How can the distance formula be derived from the Pythagorean Theorem?
4. What is the formula for the magnitude of a vector in terms of its components?
5. How do you find the midpoint of a segment between two points?

Tip: To calculate the distance between two points, always break the problem into horizontal and vertical differences first (i.e., $\Delta x$ and $\Delta y$), and then use the Pythagorean Theorem.