Equation of a Plane Given a Line in the Plane - Example 3, medium

How to find the equation of a plane if you are given the equation of a line embedded into the plane, as well as a point in the plane. You can use the line to determine the line's direction vector. Then you can use the point provided (as well as a point also on the line provided) to help to create another vector that is in the plane. We then take the cross product of the two vectors, and you have a vector that is normal to the plane. Once we have a point that is in the plane, and the normal vector to the plane, then we can write the equation of the plane in either standard form or zero
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[@grahamsell3863]

Finally an explanation that I can actually follow. Thanks for the vids

[@clementchidozie4009]

I am really glad i came across your videos!
They are really apt and easy to understand. Thanks for your efforts!!!

[@Cooked1]

you for sure explain this better than anyone else

[@kamvc72]

Just solved a question with the help of this video. thanx

[@elizabethlanier7215]

thank u soo much it turns out my proffessor didnt teach this part that I NEED!!!

[@jarredcool9391]

Your video helped me out so much. Thanks

[@sarahswalez5311]

Nice explanation. Thanks

[@chenqu773]

Verrrrrrry clearly explained !

[@KiwiOverlord]

Your videos are great
Thanks Man!

[@fireflylectures]

KiwiOverlord - Thanks for the kind words! :)

[@nournona3450]

u makin it much easier

[@raneenkakar3144]

Waoh, you’re amazingggg!!!✨

[@babybean768]

Thank you so much this was so helpful 😭🙏

[@user_used123]

Very helpful! but what if we had vector and point only i.e we don't have a line on the plane, how do we do that?

[@duncans8733]

great video here

[@devalpatel9198]

Thanks man

[@hangkertzy9722]

thankyou so much!

[@MJsMoonwalker4life]

thank you !

[@subakannan3085]

thanks for this stuff sir

[@sarashi6663]

thank you so much for this! you totally saved me

[@김진우-c4r7f]

thank you lad

[@raghavsharma4413]

You are cool man

[@nournona3450]

thank you so much

[@i_am_dumb1070]

Please make a video on projection of a lime on plane

[@mdminhajalamdip4372]

Thanks❤️

[@margerasmio4894]

is cross multiplying vectors interchangeable?

[@josephrasmussen8832]

doing them in opposite order will change the sign. Look up the "right hand rule" to find the correct order.

[@avrillavigne14]

I got a question
how to find parametric equation from lines x=2t ,y=3t,z=1+t to a plain (x-4)/-2=y/3=(z-5)/1
Can you make a video for this type of question?

[@chacelarsen50]

thanks again!!

[@samdaniels8935]

I'm so messed up on this. If I do QP instead of PQ, it doesn't come out right...but I don't understand why that wouldn't work.
edit: nevermind, it comes out either way, I just made an arithmetic mistake *facepalm*

[@mahmoudshoukry2736]

شكرا يا معلم

[@fireflylectures]

Mahmoud - you are very welcome.

[@mahmoudshoukry2736]

+Firefly Lectures thanks my proff

[@itswiftyy]

At the last bit if you do the cross product the other way around ie. v x PQ you get the vector (17,-14,16) which is just your vector *-1. Is this still correct and does the order matter?

[@gabor6259]

The order doesn't matter. The right side of the equation is 0 and -1*0 = 0.

[@Adrian-mb6ej]

if i have 2 points like P(2,1,0) and Q(0,2,0) and a line: x/2=y-2/3=2/4 ?

[@Jasonclaython]

I love you man, no homo

[@suryasapkota4043]

5-z

[@VarunChheda-u6j]

fuckin goof (-17z-2j-12k)

[@gavinburgess4374]

u r very cute r u single???? :))))))