https://file.aiquickdraw.com/mathbot/file/1726620230295dpm7nyei.png

 Part (a)   
What is the magnitude of C⃗ =A⃗ +B⃗ 
? 

In the image, the problem asks for the magnitude of vector \( \vec{C} = \vec{A} + \vec{B} \). The vectors provided are:

\[
\vec{A} = -4.66 \hat{i} - 3.02 \hat{j}
\]
\[
\vec{B} = -2.47 \hat{i} - 4.49 \hat{j}
\]

To find the magnitude of \( \vec{C} \), we first need to add the components of \( \vec{A} \) and \( \vec{B} \):

\[
\vec{C} = \vec{A} + \vec{B} = (-4.66 + -2.47) \hat{i} + (-3.02 + -4.49) \hat{j}
\]
\[
\vec{C} = -7.13 \hat{i} - 7.51 \hat{j}
\]

The magnitude \( |\vec{C}| \) is given by:

\[
|\vec{C}| = \sqrt{(-7.13)^2 + (-7.51)^2}
\]

Let's calculate the magnitude.The magnitude of \( \vec{C} = \vec{A} + \vec{B} \) is approximately \( 10.36 \).

Do you have any questions, or would you like more details on the calculations?

Here are some related questions:
1. What is the angle of vector \( \vec{C} \) from the positive x-axis?
2. How do you subtract vectors to find \( \vec{D} = \vec{A} - \vec{B} \)?
3. What is the magnitude of vector \( \vec{D} = \vec{A} - \vec{B} \)?
4. What is the direction of vector \( \vec{D} \) relative to the x-axis?
5. How do you calculate the angle between two vectors?

**Tip:** To add or subtract vectors, combine their corresponding components (i.e., x-components with x-components and y-components with y-components).

What is the magnitude of C⃗ = A⃗ + B⃗ ? The vectors are A = (-4.66 î - 3.02 ĵ) and B = (-2.47 î - 4.49 ĵ).

Learn how to calculate the magnitude of vector C⃗, which is the result of adding two vectors A⃗ and B⃗. The vectors A = (-4.66 î - 3.02 ĵ) and B = (-2.47 î - 4.49 ĵ) are combined, and the magnitude of the resulting vector C⃗ is found using the Pythagorean theorem.

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