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i need to find magnitude of vector c, i have vector A of 40 units pointing out and vector b of 50 units pointing out, there is 60 degrees between them and vector C = A-B

To find the magnitude of vector \(\vec{C}\), where \(\vec{C} = \vec{A} - \vec{B}\), we can apply the law of cosines. Since the angle between vectors \(\vec{A}\) and \(\vec{B}\) is 60 degrees, the formula for the magnitude of \(\vec{C}\) is:

\[
|\vec{C}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 - 2 \cdot |\vec{A}| \cdot |\vec{B}| \cdot \cos(\theta)}
\]

where:
- \(|\vec{A}|\) is the magnitude of vector \(\vec{A}\) (40 units),
- \(|\vec{B}|\) is the magnitude of vector \(\vec{B}\) (50 units),
- \(\theta\) is the angle between \(\vec{A}\) and \(\vec{B}\), which is 60 degrees.

Let's calculate step-by-step:

1. First, convert the angle to radians if needed, but since the cosine function works with degrees, we can directly calculate:
   \[
   \cos(60^\circ) = 0.5
   \]

2. Now, substitute the values into the formula:
   \[
   |\vec{C}| = \sqrt{40^2 + 50^2 - 2 \cdot 40 \cdot 50 \cdot 0.5}
   \]
   \[
   |\vec{C}| = \sqrt{1600 + 2500 - 2000}
   \]
   \[
   |\vec{C}| = \sqrt{4100 - 2000} = \sqrt{2100}
   \]

3. Calculate the square root of 2100:
   \[
   |\vec{C}| \approx 45.83 \, \text{units}
   \]

Thus, the magnitude of vector \(\vec{C}\) is approximately **45.83 units**.

Would you like more details on this calculation or have any questions?

Here are 5 related questions:
1. How would the magnitude change if the angle between \(\vec{A}\) and \(\vec{B}\) were different?
2. How can you represent vector \(\vec{C}\) graphically?
3. Can you solve the problem using vector components?
4. What would the magnitude of \(\vec{C}\) be if the angle between \(\vec{A}\) and \(\vec{B}\) were 90 degrees?
5. How would the magnitude of \(\vec{C}\) change if both \(\vec{A}\) and \(\vec{B}\) had the same magnitude?

**Tip:** In vector subtraction, understanding the relative angle between vectors is key to determining their resultant magnitude.

Vectors A and B are shown. What is the magnitude of a vector C if C = A - B?

In this problem, we calculate the magnitude of vector C, where C = A - B, using vector subtraction and the law of cosines. Vector A has a magnitude of 40 units, vector B has a magnitude of 50 units, and the angle between them is 60 degrees. Learn how to solve this step-by-step.

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