Find the unit vector in the direction of $$ \mathbf{v} $$. $$ \mathbf{v}=-7.1 \mathbf{i}+3.5 \mathbf{j} $$ $$ \mathbf{u}= $$

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To find the **unit vector** $$ \mathbf{u} $$ in the direction of the vector $$ \mathbf{v} = -7.1\,\mathbf{i} + 3.5\,\mathbf{j} $$, follow these steps:

### 1. **Calculate the Magnitude of $$ \mathbf{v} $$**

The magnitude (or length) of $$ \mathbf{v} $$ is given by:

$$
\|\mathbf{v}\| = \sqrt{(-7.1)^2 + (3.5)^2}
$$

$$
\|\mathbf{v}\| = \sqrt{50.41 + 12.25} = \sqrt{62.66} \approx 7.915
$$

### 2. **Divide Each Component of $$ \mathbf{v} $$ by Its Magnitude**

The unit vector $$ \mathbf{u} $$ in the direction of $$ \mathbf{v} $$ is obtained by dividing each component of $$ \mathbf{v} $$ by $$ \|\mathbf{v}\| $$:

$$
\mathbf{u} = \frac{\mathbf{v}}{\|\mathbf{v}\|} = \frac{-7.1\,\mathbf{i} + 3.5\,\mathbf{j}}{7.915}
$$

$$
\mathbf{u} = \left( \frac{-7.1}{7.915} \right)\mathbf{i} + \left( \frac{3.5}{7.915} \right)\mathbf{j}
$$

$$
\mathbf{u} \approx -0.896\,\mathbf{i} + 0.443\,\mathbf{j}
$$

### 3. **Final Answer**

$$
\boxed{\,\mathbf{u} \approx -0.896\,\mathbf{i} + 0.443\,\mathbf{j}\,}
$$

This unit vector $$ \mathbf{u} $$ has a magnitude of 1 and points in the same direction as the original vector $$ \mathbf{v} $$.
The unit vector in the direction of $$ \mathbf{v} = -7.1\,\mathbf{i} + 3.5\,\mathbf{j} $$ is approximately $$ \mathbf{u} \approx -0.896\,\mathbf{i} + 0.443\,\mathbf{j} $$.

Find the unit vector in the direction of .

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