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If a plane is parallel to the $x$ axis then it's perpendicular to the $YZ$ plane. That's what my book is saying but I have a question. If a plane is parallel to the $X$ axis then shouldn't it be also in parallel to the $Y$ axis thus it's also perpendicular to $XZ$ axis ?? Can someone explain it to me ?

TShiong
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user8700093
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  • the plane $y+z=1$ is parallel to the $x$-axis since no point of the form $(a,0,0)$ satisfies the equation of the plane. On the other hand, the plane intersects the $y$-axis at $(0,1,0)$ so is not parallel to the $y$-axis. – Lozenges Oct 20 '17 at 08:04

2 Answers2

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There are many planes parallel to the $x$-axis, but the common property of all of them is that their normal vector lies in the $yz$-plane. Now consider that planes are defined to be orthogonal iff their normal vectors are, and you get the result.

Arthur
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Since x-axis is perpendicular to yz plane,then any line parallel with x-axis would also be perpendicular to yz plane. Therefore any plane containing a line perpendicular to another plane (yz) would also be perpendicular to that plane.

WindSoul
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