The magnitude (or length) of a vector $\vec{u} = (x, y)$ is given by the formula:

$|\vec{u}| = \sqrt{x^2 + y^2}$

For the vector $\vec{u} = (-5, 3)$, we substitute $x = -5$ and $y = 3$ into the formula:

$|\vec{u}| = \sqrt{(-5)^2 + 3^2}$ $|\vec{u}| = \sqrt{25 + 9}$ $|\vec{u}| = \sqrt{34}$

So, the exact magnitude of $\vec{u}$ is:

$|\vec{u}| = \sqrt{34}$

If you'd like the approximate value, we can calculate it as:

$|\vec{u}| \approx 5.83$

Tip: When calculating the magnitude of a vector, remember that the square of each component (whether positive or negative) will always contribute positively to the result.

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Would you like further explanation or clarification? Here are some related questions for you:

1. How would the magnitude change if the components of the vector were different?
2. How do you find the direction of a vector, given its components?
3. What is the difference between the magnitude and the unit vector of a vector?
4. How would you find the magnitude of a 3D vector?
5. What happens to the magnitude of a vector if one of its components is zero?

Let me know if you'd like to dive into any of these!