The problem asks to find the component form of a vector $\vec{v}$ and round the answers to the nearest hundredth.

Let's analyze the image and proceed with the solution.

Analysis:

The vector $\vec{v}$ is shown as pointing in a specific direction in the coordinate plane. The angle given appears to be in standard position with reference to the positive $x$-axis.

General Approach:

To express a vector $\vec{v}$ in component form, we use: $\vec{v} = \langle v_x, v_y \rangle$ Where:

• $v_x = |\vec{v}| \cos(\theta)$
• $v_y = |\vec{v}| \sin(\theta)$

Here, $\theta$ is the angle made with the positive $x$-axis, and $|\vec{v}|$ is the magnitude of the vector.

Next Steps:

Please clarify:

1. The angle $\theta$ in the problem (in degrees or radians).
2. The magnitude $|\vec{v}|$ (if given).

Once I have those details, I can compute the component form for you!

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Do you have any questions so far or want more details? Here are some related questions to think about:

1. How do you determine the direction of a vector from an angle?
2. What are some common mistakes when calculating vector components?
3. How does changing the angle affect the vector's components?
4. How do we use trigonometric functions to convert between polar and rectangular coordinates?
5. Why is it important to round answers to the nearest hundredth?

Tip: Always double-check your angle orientation to ensure the correct signs for the components!