The vector -5.2A has a magnitude of 31 m and points in the positive z direction. nns N A Express your answer using two significant figures. A, = Submit Request Answer Part B Find the magnitude of the vector A Express your answer using two significant figures.

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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Educational Website: Vector Components and Magnitude**

### Example Problem: Vector Components and Magnitude

#### Given Information:
- A vector \(\mathbf{A}\) has a magnitude of 31 meters and points in the positive z direction.

#### Task:
- Find the components of the vector \(\mathbf{A}\) and its magnitude.

### Part A:
**Find the z-component of the vector \(\mathbf{A}\)**

Express your answer using two significant figures.

\[
A_z = \_\_\_\_\_ \text{ m}
\]

<div style="display: flex; align-items: center;">
    <input type="text" placeholder="Enter your answer" style="width: 200px; margin-right: 10px;">
    <button>Submit</button>
</div>

#### Part B:
**Find the magnitude of the vector \(\mathbf{A}\)**

Express your answer using two significant figures.

\[
|\mathbf{A}| = \_\_\_\_\_ \text{ m}
\]

<div style="display: flex; align-items: center;">
    <input type="text" placeholder="Enter your answer" style="width: 200px; margin-right: 10px;">
    <button>Submit</button>
</div>

**Explanation:**

Since vector \(\mathbf{A}\) points in the positive z-direction and has a magnitude of 31 meters:
- The z-component \(A_z\) will be equal to the magnitude of the vector \(\mathbf{A}\), which is 31 meters.
- The components in the x and y directions will be zero.

So, in conclusion:
\[ A_z = 31 \, \text{m} \]
\[ |\mathbf{A}| = 31 \, \text{m} \]

You can practice these steps using the input fields provided and check your answers by clicking the "Submit" button.
Transcribed Image Text:**Educational Website: Vector Components and Magnitude** ### Example Problem: Vector Components and Magnitude #### Given Information: - A vector \(\mathbf{A}\) has a magnitude of 31 meters and points in the positive z direction. #### Task: - Find the components of the vector \(\mathbf{A}\) and its magnitude. ### Part A: **Find the z-component of the vector \(\mathbf{A}\)** Express your answer using two significant figures. \[ A_z = \_\_\_\_\_ \text{ m} \] <div style="display: flex; align-items: center;"> <input type="text" placeholder="Enter your answer" style="width: 200px; margin-right: 10px;"> <button>Submit</button> </div> #### Part B: **Find the magnitude of the vector \(\mathbf{A}\)** Express your answer using two significant figures. \[ |\mathbf{A}| = \_\_\_\_\_ \text{ m} \] <div style="display: flex; align-items: center;"> <input type="text" placeholder="Enter your answer" style="width: 200px; margin-right: 10px;"> <button>Submit</button> </div> **Explanation:** Since vector \(\mathbf{A}\) points in the positive z-direction and has a magnitude of 31 meters: - The z-component \(A_z\) will be equal to the magnitude of the vector \(\mathbf{A}\), which is 31 meters. - The components in the x and y directions will be zero. So, in conclusion: \[ A_z = 31 \, \text{m} \] \[ |\mathbf{A}| = 31 \, \text{m} \] You can practice these steps using the input fields provided and check your answers by clicking the "Submit" button.
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