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The problem asks for the dot product \( A \cdot B \) of two vectors:

- Vector \( A = 3i + 2j + 4k \)
- Vector \( B = 2i - 4j + 5k \)

The dot product formula is:

\[
A \cdot B = (a_1 \times b_1) + (a_2 \times b_2) + (a_3 \times b_3)
\]

where \( A = a_1i + a_2j + a_3k \) and \( B = b_1i + b_2j + b_3k \).

Let's apply the values from the vectors:

\[
A \cdot B = (3 \times 2) + (2 \times -4) + (4 \times 5)
\]

Now let's calculate:

\[
A \cdot B = 6 + (-8) + 20 = 6 - 8 + 20 = 18
\]

Thus, the value of \( A \cdot B \) is **18**.

Do you want any more details or have any questions about this solution? 

Here are 5 related questions for further exploration:
1. How is the dot product of two vectors used in physics?
2. What is the geometric interpretation of the dot product?
3. Can the dot product of two vectors ever be negative? Under what conditions?
4. How is the angle between two vectors related to their dot product?
5. How does the dot product differ from the cross product?

**Tip**: The dot product of two vectors provides a scalar result and is directly related to the projection of one vector onto another.

Berapakah nilai A.B dari vektor A = 3i + 2j + 4k, vektor B = 2i - 4j + 5k

This page explains how to find the dot product of two vectors A = 3i + 2j + 4k and B = 2i - 4j + 5k using the formula A . B = a1*b1 + a2*b2 + a3*b3. It includes a detailed step-by-step solution and is suitable for students in Grades 9-12.

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