Let's solve this step by step based on the problem shown in the image:

Problem

We are tasked to find a vector $\mathbf{v}$ with a given magnitude $\| \mathbf{v} \| = 3$ and in the same direction as $\mathbf{u} = (0, -1, -1, 4)$.

Step 1: Normalize the vector $\mathbf{u}$

To create a vector in the same direction as $\mathbf{u}$, we first compute the unit vector $\mathbf{u}_{\text{unit}}$ by dividing $\mathbf{u}$ by its magnitude.

1. Magnitude of $\mathbf{u}$:

   $\| \mathbf{u} \| = \sqrt{(0)^2 + (-1)^2 + (-1)^2 + (4)^2} = \sqrt{0 + 1 + 1 + 16} = \sqrt{18} = 3\sqrt{2}$

2. Unit vector $\mathbf{u}_{\text{unit}}$:

   Divide each component of $\mathbf{u}$ by $\| \mathbf{u} \|$:

   = \left( 0, \frac{-1}{3\sqrt{2}}, \frac{-1}{3\sqrt{2}}, \frac{4}{3\sqrt{2}} \right).$$

Step 2: Scale the unit vector to magnitude 3

To make the vector $\mathbf{v}$ have a magnitude of 3, multiply the unit vector $\mathbf{u}_{\text{unit}}$ by 3: