I'm having trouble with these types of questions. I have the following vector $u = (4, 7, -9)$ and it wants me to find 2 vectors that are perpendicular to this one.
I know that $(4,7,-9)\cdot (x,y,z) = 0$.
The dot product of two vectors must equal to zero in order for them to be perpendicular.
But that doesn't tell me much at this point. Any inputs?
Best Answer
You are correct that your first vector needs to have dot product zero with $(4,7,-9)$. Just pick any $x,y$ you like and solve for $z$. I will pick $x=9,y=0$ and find $z=4$ works, so we have $(9,0,4)$ Now you can either do the same with dot products with both vectors, or you can take the cross product, which is guaranteed to be perpendicular to both. So take $(4,7,-9) \times (9,0,4)$ getting $(28, -97, -63)$. I admit, I used Alpha do do the work.