To find a vector perpendicular to $\begin{bmatrix} a \\ b \end{bmatrix}$, you can switch the components and change the sign of one of them. If $\begin{bmatrix} a \\ b \end{bmatrix}$ is a vector, a perpendicular vector is:

$\begin{bmatrix} -b \\ a \end{bmatrix} \quad \text{or} \quad \begin{bmatrix} b \\ -a \end{bmatrix}.$

This works because the dot product between the two vectors will be zero, confirming they are perpendicular.

Would you like more details, or do you have any questions?

Here are some related questions to explore:

1. How do you verify that two vectors are perpendicular?
2. Why does switching components and changing the sign work to find a perpendicular vector in 2D?
3. Can you generalize this method for vectors in 3D space?
4. How can you find a vector perpendicular to two given vectors in 3D?
5. What is the geometric significance of a perpendicular vector in vector fields?

Tip: For any vector $\begin{bmatrix} a \\ b \end{bmatrix}$, perpendicular vectors ensure the dot product equals zero.