https://file.aiquickdraw.com/mathbot/file/1730749031758g0ckmzvg.jpg

To find a unit vector in the same direction as vector \(\mathbf{a} = (6, 9, 4)\), we follow these steps:

1. **Calculate the Magnitude of \(\mathbf{a}\):**
   The magnitude \(|\mathbf{a}|\) of vector \(\mathbf{a}\) is given by:
   \[
   |\mathbf{a}| = \sqrt{6^2 + 9^2 + 4^2} = \sqrt{36 + 81 + 16} = \sqrt{133}
   \]
   So, \(|\mathbf{a}| = \sqrt{133}\).

2. **Divide Each Component by the Magnitude:**
   A unit vector in the same direction as \(\mathbf{a}\) is:
   \[
   \mathbf{u} = \frac{\mathbf{a}}{|\mathbf{a}|} = \left( \frac{6}{\sqrt{133}}, \frac{9}{\sqrt{133}}, \frac{4}{\sqrt{133}} \right)
   \]

Thus, the unit vector in the same direction as \(\mathbf{a}\) is approximately:
\[
\left( \frac{6}{\sqrt{133}}, \frac{9}{\sqrt{133}}, \frac{4}{\sqrt{133}} \right)
\]

Let me know if you would like a more detailed explanation, have any questions, or need further clarification!

### Related Questions
1. What is the significance of a unit vector?
2. How do we calculate the magnitude of a 3-dimensional vector?
3. Can you find a unit vector in the opposite direction of \(\mathbf{a}\)?
4. What does it mean geometrically for two vectors to be in the same direction?
5. How can we verify that the vector we found is indeed a unit vector?

**Tip:** To simplify computations, you can leave square roots in the denominator for exact answers or rationalize if required for specific applications.

Find a unit vector in the same direction as \( \mathbf{a} = (6, 9, 4) \).

Learn how to find a unit vector in the same direction as the vector a = (6, 9, 4). This example covers calculating the magnitude of a vector and obtaining a unit vector. Suitable for high school students in Grades 10-12.

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