A vector A is directed along the positive x-axis and has a magnitude of 3.00 units. Vector B is directed along the negative x-axis and has a magnitude of 2.00 units. The magnitude and direction of the vector B – A is

Group of answer choices

3.00 units in the positive x direction

1.00 unit in the positive x direction.

3.00 units in the negative x direction.

5.00 units in the negative x direction.

To solve for the vector **B - A**, we need to consider both the magnitudes and directions of vectors **A** and **B**.

### Step 1: Express the vectors in component form.
- **A** is directed along the positive x-axis and has a magnitude of 3.00 units. Therefore, the vector **A** in component form is:
  \[
  \mathbf{A} = +3.00 \, \hat{i}
  \]
  
- **B** is directed along the negative x-axis and has a magnitude of 2.00 units. Therefore, the vector **B** in component form is:
  \[
  \mathbf{B} = -2.00 \, \hat{i}
  \]

### Step 2: Subtract vectors (B - A).
Now, subtract vector **A** from vector **B**:
\[
\mathbf{B} - \mathbf{A} = (-2.00 \, \hat{i}) - (+3.00 \, \hat{i})
\]
\[
\mathbf{B} - \mathbf{A} = -2.00 \, \hat{i} - 3.00 \, \hat{i} = -5.00 \, \hat{i}
\]

### Step 3: Analyze the result.
The resulting vector has a magnitude of 5.00 units and is directed along the negative x-axis.

### Final Answer:
The magnitude and direction of vector **B - A** is:
\[
\boxed{5.00 \, \text{units in the negative x direction.}}
\]

Let me know if you would like further details or clarifications!

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Here are 5 related questions for practice:
1. What would be the result of **A - B** instead of **B - A**?
2. How would the result change if vector **A** had a magnitude of 4 units?
3. What is the resultant vector if **A** is directed along the y-axis instead of the x-axis?
4. How do you find the magnitude of a vector in 2D space?
5. What happens to the magnitude of a vector if both vectors are doubled?

**Tip:** When subtracting vectors, always pay close attention to the directions, as they are as important as magnitudes in vector calculations.

A vector A is directed along the positive x-axis and has a magnitude of 3.00 units. Vector B is directed along the negative x-axis and has a magnitude of 2.00 units. The magnitude and direction of the vector B – A is?

Learn how to find the magnitude and direction of the vector B - A, where vector A is directed along the positive x-axis with a magnitude of 3.00 units, and vector B is along the negative x-axis with a magnitude of 2.00 units. This problem demonstrates vector subtraction and is suitable for students in Grades 10-12.

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