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?

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.