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.