Question

Find the equation of the plane containing the points (2,0,0) (0,6,0) and (0,0,5) in the form of ax+by+cz=D

Answer 1

what is a vector normal to the plane passing through the given points?

Answer 2

hint:
if we substitute the coordinates of the given points into the equation:
\[ax + by + cz = d\]
we get the subsequent linear system:
\[\left\{ \begin{gathered}
2a = d \hfill \\
6b = d \hfill \\
5c = d \hfill \\
\end{gathered} \right.\]
which has \(\infty\) solutions. Please solve such linear system