A line goes through point $A = (9, -7, 31)$ and the line is perpendicular to vectors $[7, 1, 2]$ and $[3, 0, 1]$.
What is the equation of the line?
The cross product of $[7, 1, 2]$ and $[3, 0, 1]$ is $[1, -1, -3]$.
I believe the line can be written as $x = [9, -7, 31] + t [1, -1, -3]$, where $t$ is a real number.
I'm somewhat skeptical of my own work. If you find the cross product (which will be perpendicular to the two given vectors); why does that mean it is automatically parallel with the line that is also perpendicular to these two vectors?
Given the vectors are in three-dimensional space; is it possible to produce a cross product of these two vectors and that vector not to be parallel with the line I found?