Review the graph.

On a coordinate plane, vector u has origin (negative 2, 3) and terminal point (6, 3).

What are the characteristics of the vector shown?

magnitude of 8 and direction angle equal to 0°
magnitude of 8 and direction angle equal to 180°
magnitude of 2 StartRoot 2 EndRoot and direction angle equal to 0°
magnitude of 2 StartRoot 2 EndRoot and direction angle equal to 180°

To analyze the vector \( \vec{u} \), we’ll calculate its characteristics using its origin and terminal points.

### Step 1: Determine the Vector Components
The vector \( \vec{u} \) has an origin at \( (-2, 3) \) and a terminal point at \( (6, 3) \). The components of \( \vec{u} \) can be calculated as:
\[
\vec{u} = (x_2 - x_1, y_2 - y_1) = (6 - (-2), 3 - 3) = (8, 0)
\]

### Step 2: Calculate the Magnitude
The magnitude of \( \vec{u} \) is given by:
\[
|\vec{u}| = \sqrt{(8)^2 + (0)^2} = \sqrt{64} = 8
\]

### Step 3: Determine the Direction Angle
Since the vector lies on the x-axis and moves to the right (positive x-direction), its direction angle is \( 0^\circ \).

### Conclusion
The vector \( \vec{u} \) has:
- **Magnitude of 8**
- **Direction angle of \( 0^\circ \)**

### Answer
The correct option is:
**Magnitude of 8 and direction angle equal to \( 0^\circ \)**

Would you like further clarification on any steps?

Here are some related questions to extend understanding:
1. How would the vector’s direction angle change if it pointed left instead of right?
2. What would the magnitude be if the vector spanned from (6, 3) to (-2, 3)?
3. How can we find a unit vector with the same direction as \( \vec{u} \)?
4. How does the magnitude change if the vector's components double?
5. What would the direction angle be for a vector lying on the y-axis?

**Tip:** A vector lying entirely on the x-axis has a direction angle of \( 0^\circ \) if it points to the right and \( 180^\circ \) if it points to the left.

On a coordinate plane, vector u has origin (negative 2, 3) and terminal point (6, 3). What are the characteristics of the vector shown? 

Options: 
1. Magnitude of 8 and direction angle equal to 0° 
2. Magnitude of 8 and direction angle equal to 180° 
3. Magnitude of 2√2 and direction angle equal to 0° 
4. Magnitude of 2√2 and direction angle equal to 180°

Explore the characteristics of a vector from (-2, 3) to (6, 3), including its magnitude and direction. This problem involves calculating vector components, determining magnitude, and understanding direction angles. Ideal for students in Grades 9-10.

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