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What is the  x
  component of the vector sum  V⃗ =A⃗ +B⃗ +C⃗ 
 ? 

The vectors given are:

\[
\vec{A} = (1.21) \hat{i} + (4.42) \hat{j} + (8.28) \hat{k}
\]
\[
\vec{B} = (-10.04) \hat{i} + (1.29) \hat{j} + (3.81) \hat{k}
\]
\[
\vec{C} = (11.59) \hat{i} + (-2.58) \hat{j} + (3.31) \hat{k}
\]

The vector sum \(\vec{V} = \vec{A} + \vec{B} + \vec{C}\) will involve adding the components of \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\) for the \(\hat{i}\), \(\hat{j}\), and \(\hat{k}\) directions separately.

To find the x-component (which corresponds to the \(\hat{i}\) direction) of the vector sum \(\vec{V}\), we simply add the x-components of \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\).

The x-components are:
- \(\vec{A}_x = 1.21\)
- \(\vec{B}_x = -10.04\)
- \(\vec{C}_x = 11.59\)

Now, summing them:

\[
V_x = 1.21 + (-10.04) + 11.59
\]

Let's calculate this.The x-component of the vector sum \(\vec{V} = \vec{A} + \vec{B} + \vec{C}\) is approximately \(2.76\).

Would you like further details or have any questions?

Here are five related questions:
1. How do you calculate the y-component of the vector sum \(\vec{V}\)?
2. What is the full vector form of \(\vec{V}\)?
3. How do you compute the magnitude of a vector from its components?
4. Can you find the dot product of two vectors like \(\vec{A} \cdot \vec{B}\)?
5. How do you calculate the cross product of two vectors?

**Tip:** When summing vectors, always handle the components in each direction (\(\hat{i}\), \(\hat{j}\), \(\hat{k}\)) independently.

What is the x component of the vector sum V⃗ =A⃗ +B⃗ +C⃗ ?

Learn how to calculate the x component of the vector sum V = A + B + C using component-wise addition. This problem involves vector addition, focusing on the î component, and is suitable for students in Grades 10-12.

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