[9, 7] is the difference between 2 vectors with components [3, 4] and [-6, b]. What is b?

We are given that the difference between two vectors \([3, 4]\) and \([-6, b]\) is \([9, 7]\). 

The difference between two vectors is calculated component-wise:

\[
\text{Vector 1} - \text{Vector 2} = \left( [3, 4] - [-6, b] \right) = [9, 7]
\]

This can be broken down into two equations based on their components:

1. \(3 - (-6) = 9\)
2. \(4 - b = 7\)

Let's solve each equation:

1. \(3 - (-6) = 3 + 6 = 9\) (this is true)
2. \(4 - b = 7\)

Now, solve for \(b\):

\[
4 - b = 7 \implies b = 4 - 7 = -3
\]

Thus, \(b = -3\).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the sum of the vectors \([3, 4]\) and \([-6, -3]\)?
2. How do you find the magnitude of a vector?
3. How do you calculate the dot product of two vectors?
4. Can the difference of two vectors be a zero vector?
5. What is a unit vector, and how is it calculated?

**Tip:** When solving vector equations, handle each component separately for clarity.

The query submitted by the user: [9, 7] is the difference between 2 vectors with components [3, 4] and [-6, b]. What is b?

Learn how to solve for the missing vector component in the vector subtraction problem [9, 7] = [3, 4] - [-6, b]. This detailed explanation covers key concepts in vector subtraction and component-wise calculation, suitable for students in Grades 8-10.

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