# Why line passing through origin in the intersection of three planes is parallel to the planes?

• There are three planes $P_1, P_2$ and $P_3$ and they all pass through origin so it will have infinite solutions.

• The normal to these planes $n_1, n_2$ and $n_3$ are coplanar.

• The line passing though origin is perpendicular to normal vectors but is parallel to three planes.

Why is that line passing through origin parallel to the three planes?