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.