Please show the following given that A = (0,6,3), B = 2ax+3ay+5az, C= (1,4,7), D = ay+2az 

A+B	

We are given the following vectors:

- \( A = (0, 6, 3) \)
- \( B = 2a \hat{i} + 3a \hat{j} + 5a \hat{k} \)
- \( C = (1, 4, 7) \)
- \( D = a \hat{j} + 2a \hat{k} \)

Now, to calculate \( A + B \), we add the corresponding components of the vectors.

### Breaking down the vectors:

- Vector \( A \) is \( (0 \hat{i}, 6 \hat{j}, 3 \hat{k}) \)
- Vector \( B \) is \( (2a \hat{i}, 3a \hat{j}, 5a \hat{k}) \)

The sum \( A + B \) is:

\[
A + B = (0 + 2a) \hat{i} + (6 + 3a) \hat{j} + (3 + 5a) \hat{k}
\]

Thus, we get:

\[
A + B = (2a, 6 + 3a, 3 + 5a)
\]

This is the resulting vector for \( A + B \).

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Would you like to explore any other operations involving these vectors, or further details?

Here are 5 related questions to expand this topic:

1. What is the magnitude of vector \( A + B \)?
2. Can we find \( A - B \)?
3. How do we calculate the dot product of \( A \) and \( B \)?
4. What is the cross product of vectors \( A \) and \( B \)?
5. Can we express \( C + D \) similarly?

**Tip:** When adding vectors, always ensure the components along each axis are aligned properly for accurate results.

Please show the following given that A = (0,6,3), B = 2ax+3ay+5az, C= (1,4,7), D = ay+2az. A + B

Explore the addition of two vectors, A = (0,6,3) and B = 2ax + 3ay + 5az, by performing component-wise addition. Learn key concepts in vector operations, including the vector addition rule, and how to compute the resultant vector step by step. Suitable for Grades 10-12.

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