Are
\begin{equation*}
-x-4y+3z=-9~\text{and}~x+4y-3z=6
\end{equation*}
equations of the same plane? I graphed them and they look the same, but I am not sure. Thanks
[Math] Equations of the same plane
linear algebravector-spaces
linear algebravector-spaces
Are
\begin{equation*}
-x-4y+3z=-9~\text{and}~x+4y-3z=6
\end{equation*}
equations of the same plane? I graphed them and they look the same, but I am not sure. Thanks
Best Answer
Two equations $$ax+by+cz = d$$ and $$a'x+b'y+c'z=d'$$ represent the same plane if there exists $\lambda \neq 0$ such that $(a',b',c',d') = \lambda(a,b,c,d)$. In other words, if you can re-scale one equation to get the other one. This don't happen here.