## Problem on finding a perpendicular vector

Find a vector perpendicular to $\langle1, 2, 3 \rangle$.
• ## Solution

We recall that
For this problem, we will take the cross product of $\langle 1, 2, 3 \rangle$ with $\langle 0, 0, 1\rangle$. The result will be perpendicular to both of these vectors.
Thus, a perpendicular vector to $\langle 1, 2, 3 \rangle$ is $\langle 2, -1, 0 \rangle.$