Equation of a Plane Parallel to a Given Plane and Containing a Point

Given a point and a plane in the space, how do we find an equation of a plane passing through that given point and parallel to that given plane?
In general, when we want to find an equation of a 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.
Let's recall that two planes are parallel if their normal vectors are parallel. So, finding the normal vector should now be easy 😉
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[@fyodor8008]

We engineers are lucky to have content providers like this

[@GlassofNumbers]

So happy to hear that! Please share with other engineers you know 😁

[@gladysmartinezfranco2267]

Great teaching style! Will apply this when taking my exam on Monday😊

[@GlassofNumbers]

Thank you! Good luck on your exam!!

Such a smooth way of teaching! Thank you!

[@GlassofNumbers]

Thank you for the comment!

[@Matt83523]

You sir, saved me from getting beat by my tutor

[@GlassofNumbers]

Good to hear my video helps! Please subscribe and share my videos to support me!!

[@alialogaily882]

Thank you, I finally understand it that was a great explanation.

[@GlassofNumbers]

Thank you for saying that! I am happy you like my explanation! Please share my videos 😁

[@harmianaaa]

Great video!

[@GlassofNumbers]

Thank you! Please help me share this video with others 😁👍

[@ElimY]

very helpful! and your handwriting is so neat omg

[@GlassofNumbers]

Thank you! Glad you like my handwriting, please share my videos to others 😁

[@anujrawat3626]

still works in 2021 :-) BTW i was searching for the vector approach, i still cant find

[@GlassofNumbers]

Thank you! Can you clarify what you meant by the vector approach?

[@anujrawat3626]

@@GlassofNumbers Actually, they Textbooks we refer is NCERT and there u'll see every qs can be done either in vector form or in Cartesian form.. yeah, but if someone Understands core concepts.. its the same for them🙂i am beginner tho

[@GlassofNumbers]

I see. I don't have access to NCERT textbooks. Now if you want your answer for the plane in vector form, you can parametrize it and write it in vector form. Have you tried that?

[@rationalpi6755]

Why does this video only have 22 views????? You explain it so well

[@GlassofNumbers]

Thank you! I think it's because my channel is relatively new. I will continue to create more videos to get more exposure. I am glad you like this video!

[@valentinaparedes8764]

Best video explaining this concept, I am a bit confused to why we can find both the orthogonal plane and the parallel plane using the same method...

[@GlassofNumbers]

@@valentinaparedes8764 Thank you! The idea of finding an equation of a plane is that we need two things: a point in the plane and the normal vector of the plane. So, the method is the same for finding an orthogonal plane or parallel plane, but there are difference in details: 1) If the plane we try to find is parallel to a given plane, then we use the same normal vectors. 2) If the plane we try to find is perpendicular to a given plane, then we use a vector parallel to the given plane as the normal vector of the plane we are trying to find.

[@fatcabbage]

Would it be the same formula when it is perpendicular as well?

[@GlassofNumbers]

The general form of the plane equation will be the same, but the way to solve the problem will be different.

[@tungstendeliz4960]

What's up everybody, i technically don't NEED calc 3 but I'm taking it for that sweet, sweet p-chem CHEMISTRY GANG CHEMISTRY GANG CHEMISTRY GANG

[@baku_3720]

Thx for the video, it helped me to understand the problem

[@GlassofNumbers]

Happy to hear my video helps 😁👍

[@JeffJia-yj1zr]

video starts at 3:29

[@JeffJia-yj1zr]

video starts at 2:29

[@nabihahsafiyahmohdazizan4995]

What about the 5 in the initial equation?

[@GlassofNumbers]

For this problem, to find the new plane, the 5 in the initial equation is not needed.

[@mudasirjan06]

This was the only yt video on this question!

[@GlassofNumbers]

Really?

[@paulwilliamson8499]

Great explanation, Thank you!

[@GlassofNumbers]

Thank you for your support!! Please share my videos to others! 😁

[@kaytlincourtney9924]

Thank you so much! This helped me better understand how to do my hw and what formulas went with what questions!

[@GlassofNumbers]

Thank you! I am happy to hear that! There are other ones about lines and planes, check them out when you prepare for the next quiz or exam 😁👍

[@quasar5538]

THANK YOU!!!

[@GlassofNumbers]

Thank you for your support!! Please help me share this video with others 😁👍

[@mrt1n.]

This was easier than I thought but the video was still helpful, thank u bro

[@GlassofNumbers]

Thank you! Yes, some of these types of problems are easy while some are more difficult!

[@JonnyMiata]

Thank you, very clear

[@GlassofNumbers]

That's great! Thank you for the comment! Please share this video with others 😁👍

[@trocks1722]

You Sir, deserve my like!👍🏽

[@GlassofNumbers]

Thank you! Glad you like it!

[@JarppaGuru]

7:59 before people wanted share. now they want money to make video. well dont do then xD

[@GlassofNumbers]

What do you mean 🤔

[@kareemelzahaby2293]

A great video I appreciate your efforts❤️❤️

[@GlassofNumbers]

Glad you like my video!! Please share this video with your friends and on Facebook! 😁

[@eyadallahham9421]

Great explanation !!!

[@GlassofNumbers]

Thank you!

[@syntax2679]

very helpful!!! Thank you!!!!

[@GlassofNumbers]

Thank you! Glad my video helps!! 😁

[@yangzhen2889]

The video is clear to understand.

[@GlassofNumbers]

Thank you! Please help me share the video with others 😁👍

[@yangzhen2889]

Yes, I will.

[@ahadjan5233]

You should be my professor.

[@GlassofNumbers]

Haha, thank you for saying that 😁👍

[@nilrohitdas9652]

Love from India bro

[@GlassofNumbers]

Thank you! 😁Please share my video!

[@prashri2272]

Superb explanation

[@GlassofNumbers]

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[@_koviao_]

I like the content

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[@timtran3170]

thanks

[@GlassofNumbers]

Please share my video to others 😁 and thank you for the comment!!

[@vihangaabeynayaka4014]

Thanx sir❤❤

[@GlassofNumbers]

Thank you! Happy New Year!

[@bagchaser3859]

Thanks

[@GlassofNumbers]

Thank you! Please share my video to others 😁

[@ZeekerDog]

thanks, needed this for calc 3

[@GlassofNumbers]

That's good! Please help me share this video with others in Calc 3 😁👍

[@jacobecker4075]

would be a great vid if you were only trying to explain the concept and not trying to reach the 8 min mark

[@GlassofNumbers]

Thank you for your comment. I wasn't trying to hit the 8 min (what's the significance of that?) It's my style of talking. But I will take consideration of your advice of being more concise.

[@jacobecker4075]

@@GlassofNumbers If its your way of explaining then its fine, still gets the concept across clearly enough. Just seemed like you were going on longer than you need to because you wanted to reach 8 min for the ad revenue, I don't like it when creatord neglect the educating part for their own gain.

[@GlassofNumbers]

Haha, there is no revenue for a small channel like mine, so going longer is not my intention. It's just that when I lecture in person and because students can't go back, I take the time. But that's not the case for video because people can just re-watch a certain part if something is unclear. I realized that just recently, but it's already after 200 videos 😅 I wish I knew about this earlier because the retention rate does suffer.

[@jacobecker4075]

@@GlassofNumbers No problem man, didn't want to sound mean. Still a very helpfull video thank you