https://file.aiquickdraw.com/mathbot/file/1730408362529ohsu0b2e.jpg

To determine the vector shown in component form, let's analyze the graph carefully.

1. The vector starts at the origin \((0, 0)\) and ends at a point that appears to be \((3, 4)\).

2. The component form of a vector is given as:
   \[
   \text{Vector} = a \mathbf{i} + b \mathbf{j}
   \]
   where \(a\) is the horizontal (x-axis) component and \(b\) is the vertical (y-axis) component.

3. From the graph, we see that:
   - The vector moves **3 units to the right** along the x-axis.
   - The vector moves **4 units up** along the y-axis.

4. Thus, the vector in component form is:
   \[
   \text{Vector} = 3 \mathbf{i} + 4 \mathbf{j}
   \]

Would you like more details on how vector components are determined?

### Related Questions:
1. How can I calculate the magnitude of a vector given its components?
2. What does it mean if a vector has a negative component?
3. How do we find the direction angle of a vector?
4. What are unit vectors, and how do they relate to components \( \mathbf{i} \) and \( \mathbf{j} \)?
5. How would the vector change if it was flipped to point in the opposite direction?

**Tip:** When determining vector components from a graph, always check the orientation (right/left for \( \mathbf{i} \) and up/down for \( \mathbf{j} \)).

Write the vector shown above in component form.

Learn how to write a vector in component form by analyzing its movement along the x and y axes. This example demonstrates finding the components of a vector based on a graph, showing the calculation of horizontal and vertical components. Suitable for high school students.

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