Equation of the Plane Containing Line of Intersection of Two Planes & Perpendicular to a Given Plane

How do we find an equation of the plane passing through two points and is perpendicular to a given plane?
In general, when we want to find an equation of the plane, we need to know a point lying in the plane, and the normal vector of the plane (which is perpendicular to the plane). We already have a point, all we need is the vector normal to the plane.
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[@duelingo8731]

ur a phenomenal human. may god bless u with eternal life

[@GlassofNumbers]

Thank you! Please help others by sharing the video! 😊

[@yoooo7568]

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[@GlassofNumbers]

Happy to hear my video helps!! Good luck on your midterm!

[@thr_9991]

Crystal clear explanation 🙏🙏

[@GlassofNumbers]

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[@krisscage]

Thank you for the great lecture.

[@GlassofNumbers]

No problem! Always happy my video helps 😁👍 please share it with others!

[@austinyong2100]

Thanks it really help me out

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[@katherinelee1022]

Thanks for the explanation! I was wondering why can't you take the cross product of the first two vectors and then take a second cross product with the last plane

[@GlassofNumbers]

We can do that too! If we take the cross product of and , we will get v1 = . And the rest will be the same as you said.

[@katherinelee1022]

@@GlassofNumbers I see thanks!

[@kabirc1211]

@@GlassofNumbers Isnt that harder though since u still need a point to define the plane so therefore have to find a line (then find a point) of intersection anyway?