https://file.aiquickdraw.com/mathbot/file/1727627546420ru6fbpnw.jpg

To find the magnitude of the vector \(\vec{u}\), we need to first determine the coordinates of its initial and terminal points from the graph.

From the image:
- The initial point of vector \(\vec{u}\) is at \((1, 7)\).
- The terminal point of vector \(\vec{u}\) is at \((7, 4)\).

The formula for the magnitude (or length) of a vector \(\vec{u} = \langle x_2 - x_1, y_2 - y_1 \rangle\) is:

\[
|\vec{u}| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the points \((x_1, y_1) = (1, 7)\) and \((x_2, y_2) = (7, 4)\):

\[
|\vec{u}| = \sqrt{(7 - 1)^2 + (4 - 7)^2}
\]

Now I will calculate the result.The magnitude of vector \(\vec{u}\) is approximately \(6.71\), rounded to the nearest hundredth.

Would you like further details or have any questions about this calculation?

Here are 5 related questions for practice:
1. How do you calculate the direction of a vector given its points?
2. What is the difference between the magnitude and direction of a vector?
3. How do you find the unit vector in the direction of a given vector?
4. Can you calculate the distance between two points using the same formula as vector magnitude?
5. What are the components of a vector if its magnitude is known?

**Tip:** Always remember to square the differences in both the x and y coordinates before adding them when calculating the magnitude of a vector.

Find the magnitude of vector u given the initial point (1, 7) and the terminal point (7, 4).

Learn how to calculate the magnitude of a vector given its initial and terminal points using the distance formula. This problem involves key vector concepts and is suitable for students in Grades 9-12.

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