https://file.aiquickdraw.com/mathbot/file/17268872363192xe241xz.jpg

To solve this problem, let's break down the information from the image:

### Given:
- A vector \( \vec{v} \) is shown at an angle of \( 26^\circ \) above the positive x-axis.
- The magnitude of the vector is 2 units.

### Goal:
We need to express the vector \( \vec{v} \) in its component form, based on its magnitude and direction. 

### Approach:
A vector \( \vec{v} \) can be expressed in component form as:
\[
\vec{v} = (v_x, v_y)
\]
where \( v_x \) is the horizontal (x-axis) component and \( v_y \) is the vertical (y-axis) component.

The horizontal and vertical components are calculated as:
- \( v_x = |\vec{v}| \cos \theta \)
- \( v_y = |\vec{v}| \sin \theta \)

Here, the magnitude \( |\vec{v}| = 2 \) and the angle \( \theta = 26^\circ \).

Thus:
- \( v_x = 2 \cos 26^\circ \)
- \( v_y = 2 \sin 26^\circ \)

### Solution:
So the vector \( \vec{v} \) in component form is:
\[
\vec{v} = (2 \cos 26^\circ, 2 \sin 26^\circ)
\]

### Correct Answer:
The correct option is **D: \( (2 \cos 26^\circ, 2 \sin 26^\circ) \)**.

Would you like further clarification or a deeper dive into any of these steps?

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Here are 5 related questions you might find useful:
1. How do you convert a vector given in magnitude and direction into its component form?
2. How do sine and cosine functions relate to vector components in a 2D plane?
3. What is the geometric interpretation of vector components?
4. How would the components change if the angle were measured from the y-axis?
5. Can you generalize the formula for converting a vector from polar to Cartesian form?

**Tip:** Always check whether the angle is measured from the x-axis or y-axis when determining vector components.

Which of the following represents the vector v shown in the figure to the right?

Learn how to represent a 2D vector in its component form based on its magnitude and direction. This example problem covers vector decomposition, trigonometry, and coordinate geometry, suitable for high school students.

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