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The problem asks you to find the sum of two vectors \(\vec{g}\) and \(\vec{p}\), where:

\[
\vec{g} = 7\hat{i} - \hat{j}
\]
\[
\vec{p} = \hat{i} + 6\hat{j}
\]

We need to add these two vectors component-wise:

1. The \(\hat{i}\) components are: \(7\hat{i}\) from \(\vec{g}\) and \(1\hat{i}\) from \(\vec{p}\). Adding these gives:
   \[
   7 + 1 = 8
   \]

2. The \(\hat{j}\) components are: \(-1\hat{j}\) from \(\vec{g}\) and \(6\hat{j}\) from \(\vec{p}\). Adding these gives:
   \[
   -1 + 6 = 5
   \]

Thus, the vector sum \(\vec{g} + \vec{p}\) is:

\[
\vec{g} + \vec{p} = 8\hat{i} + 5\hat{j}
\]

Would you like further details or have any questions?

Here are five related questions:
1. What is the magnitude of the vector sum \(\vec{g} + \vec{p}\)?
2. What is the direction (angle) of \(\vec{g} + \vec{p}\) with respect to the positive \(x\)-axis?
3. If \(\vec{g} = 7\hat{i} - \hat{j}\), what is the magnitude of \(\vec{g}\)?
4. How would you subtract two vectors, like \(\vec{g} - \vec{p}\)?
5. How can you represent vectors in three dimensions?

**Tip**: When adding vectors, always combine corresponding components (\(\hat{i}\) with \(\hat{i}\), and \(\hat{j}\) with \(\hat{j}\)).

Given \( \vec{g} = 7\hat{i} - \hat{j} \) and \( \vec{p} = \hat{i} + 6\hat{j} \), find \( \vec{g} + \vec{p} \).

Learn how to find the sum of two vectors \( \vec{g} = 7\hat{i} - \hat{j} \) and \( \vec{p} = \hat{i} + 6\hat{j} \). This problem covers key vector addition concepts and the component form of vectors. Suitable for students in Grades 9-12.

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