Parallel Vectors factor

Question

I came across what seems to be a confusing problem to me, I'm studying vector analysis and this problem is not accepting any solution. "If A=[1,2,-1] and B=[Bx,By,3], find Bx and By such that A and B are parallel". My first attempt to solve was doing cross product and set the resultant vector equals zero which yields Bx=5/9 and By = -31/36 but when i want to verify my solution by doing dot product and setting the result equals to 1 it doesn't yield 1. Is there anything i'm doing wrong here ? Any help and notes will be appreciated.

Answer 1

write $$\alpha[1;2;-1]=[bx;by;3]$$ from the last equation we get $$\alpha=-3$$ can you proceed?

Answer 2

To be parallel, we need:

$$\frac{B_x}{1}=\frac{B_y}{2}=\frac{3}{-1}\implies B_x=-3 \quad B_y=-6$$