To find the unit vector in the same direction as vector v = ⟨-5, 12⟩, we follow these steps:

1. Calculate the magnitude of v, denoted as ||v||: $||v|| = \sqrt{(-5)^2 + (12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13$

2. Divide each component of the vector by the magnitude to get the unit vector: $\text{Unit vector} = \left\langle \frac{-5}{13}, \frac{12}{13} \right\rangle$

Therefore, the unit vector in the same direction as v is: $\left\langle -\frac{5}{13}, \frac{12}{13} \right\rangle$

Let me know if you want further clarification or have any questions.

Related Questions:

1. What is the general formula to find the magnitude of a vector?
2. How do you determine if two vectors are in the same direction?
3. What is the difference between a unit vector and a regular vector?
4. Can the unit vector be negative?
5. How does finding a unit vector help in real-world applications?

Tip:

To check your unit vector calculation, ensure that its magnitude is exactly 1.