Finding Points Parallel to a Plane

[Guest2]

If the vector $P = (1,2,-1)$ is parallel to the plane $7x+2y+kz = 5$, then what's the value of $k$?

 

[Deveno]

Do you know how to find the general formula for points parallel to a plane?

 

[Guest2]

Do you know how to find the general formula for points parallel to a plane?

So we find another plane parallel to this in which the point $(1,2,-1)$ lies?

I think $\mathbf{n} \cdot (\mathbf{x-x_{0}}) = 0$ so

$<7,2,k><x-1,y-2,z+1> = 0 \\
\implies 7x+2y+kz+k = 11 \\

\therefore 11-k = 5 \\

\implies k = 6.$