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Identify the given vector.

April 19, 2026Mathematics

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Step-by-step solution

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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 $v$ .

Identify the given vector.
The given vector is $v = \begin{bmatrix} 4 \\ -2 \\ 1 \end{bmatrix}$ .
Calculate the magnitude of vector $v$ .
The magnitude of a vector $\begin{bmatrix} x \\ y \\ z \end{bmatrix}$ is given by $||v|| = \sqrt{x^2 + y^2 + z^2}$ .
$||v|| = \sqrt{4^2 + (-2)^2 + 1^2}$ $||v|| = \sqrt{16 + 4 + 1}$ $||v|| = \sqrt{21}$
Calculate the unit vector $u$ .
$u = \frac{1}{||v||} v$ $u = \frac{1}{\sqrt{21}} \begin{bmatrix} 4 \\ -2 \\ 1 \end{bmatrix}$
Compare with the given options.
The calculated unit vector matches option a.

The final answer is $\boxed{\text{a. } \frac{1}{\sqrt{21}} \begin{bmatrix} 4 \\ -2 \\ 1 \end{bmatrix}}$ .

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Identify the given vector.

Step-by-step solution

Identify the given vector.

Calculate the magnitude of vector vvv.

Calculate the unit vector uuu.

Compare with the given options.

Still stuck on this one?

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