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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[grahamsell]

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

[elizabethlanier]

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

[clementchidozie]

I am really glad i came across your videos!

They are really apt and easy to understand. Thanks for your efforts!!!

[Cooked]

you for sure explain this better than anyone else

[kamvc]

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

[jarredcool]

Your video helped me out so much. Thanks

[babybean]

Thank you so much this was so helpful 😭🙏

[sarashi]

thank you so much for this! you totally saved me <3

[user_used]

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?

[i_am_dumb]

Please make a video on projection of a lime on plane

[margerasmio]

is cross multiplying vectors interchangeable?

[avrillavigne]

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?

[samdaniels]

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*

[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?

[Adrian-mbej]

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 ?