https://file.aiquickdraw.com/mathbot/file/1726582912249tcf7xjo3.jpg

The question asks to determine the magnitude and direction of vector **C** such that the resultant of the three vectors **A**, **B**, and **C** equals zero.

We are given the vectors **A** and **B** with their magnitudes and directions based on the image. Let's first calculate these vectors and then determine vector **C**.

### Step 1: Determine vectors **A** and **B** from the image.

- **Vector A** appears to be pointing in the third quadrant (southwest) with coordinates approximately \((-5, 5)\).
- **Vector B** is in the first quadrant (northeast) with coordinates approximately \((5, 10)\).

Let's write these vectors in component form:

- \( \mathbf{A} = (-5, 5) \)
- \( \mathbf{B} = (5, 10) \)

### Step 2: Calculate vector **C** for the resultant to be zero.

Since the resultant of **A**, **B**, and **C** should be zero, we use the vector equation:

\[
\mathbf{A} + \mathbf{B} + \mathbf{C} = 0
\]

Rearranging this, we find:

\[
\mathbf{C} = - (\mathbf{A} + \mathbf{B})
\]

Let's compute this:

\[
\mathbf{C} = - [(-5, 5) + (5, 10)]
\]
\[
\mathbf{C} = - [(0, 15)] = (0, -15)
\]

### Step 3: Conclusion

- The magnitude of vector **C** is \( |\mathbf{C}| = 15 \) (as it lies entirely in the vertical direction).
- The direction of vector **C** is downward (along the negative \(y\)-axis).

Would you like more details or have any other questions?

Here are 5 related questions:
1. How can I calculate the magnitude of a vector in general?
2. What are the vector components in different coordinate systems?
3. How do vector addition and subtraction work graphically?
4. How does one find the direction of a vector using trigonometry?
5. Can you show how to find the resultant of three or more vectors?

**Tip**: When adding vectors, always break them down into components, as it simplifies the calculations.

Vektor A dan B memiliki besar dan arah seperti pada gambar di bawah. Tentukan besar dan arah vektor C sehingga resultan ketiga vektor adalah NOL.

Learn how to calculate the magnitude and direction of vector C given the vectors A and B. This problem involves vector addition and the law of vector components, and is suitable for students in Grades 10-12.

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