I have $A(-2,1,0)$ and $B(7,-2,k)$ and $$\ell: x = (-4,-5,-2)+t(1,-2,0)$$
I need to find a $k$ so that A and B and $\ell$ are in the same plane.
I thought this doesn't make sense because you can create a plane with two different lines. Therefore, I will choose each time a different $k$, will get a different line ($AB$), and I can create a plane who has inside $\ell$ and $AB$.
I don't seem to get the problem pretty well. Can someone help me please?
hint: Choose $2$ points of the line $\ell$: $C = (-4,-5,-2), D = (-3,-7,-2)$, and write an equation of the plane $\alpha$ passing through $3$ points: $A, D, C$, and then plug the coordinates of the point $B$ into the equation of the plane $\alpha$ to find $k$.