To find a unit vector $u$ in the same direction as vector $v$, we use the formula $u = \frac{v}{||v||}$, where $||v||$ is the magnitude of vector $v$. Step 1: Identify the given vector. The given vector is $v = \begin{bmatrix} 4 \\ -2 \\ 1 \end{bmatrix}$. Step 2: Calculate the magnitude of vector $v$. The magnitude of a vector $\begin{bmatrix} x \\ y \\ z \end{bmatrix}$ is given by $||v|| = \sqrt{x^2 + y^2 + z^2}$. $$ ||v|| = \sqrt{4^2 + (-2)^2 + 1^2} $$ $$ ||v|| = \sqrt{16 + 4 + 1} $$ $$ ||v|| = \sqrt{21} $$ Step 3: Calculate the unit vector $u$. $$ u = \frac{1}{||v||} v $$ $$ u = \frac{1}{\sqrt{21}} \begin{bmatrix} 4 \\ -2 \\ 1 \end{bmatrix} $$ Step 4: Compare with the given options. The calculated unit vector matches option a. The final answer is $\boxed{\text{a. } \frac{1}{\sqrt{21}} \begin{bmatrix} 4 \\ -2 \\ 1 \end{bmatrix}}$. That's 2 down. 3 left today — send the next one.