Distance Between Point and Plane - Example 1

An example working through how to compute the distance between a point and a plane.
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[@ronnies.3440]

Thanks for the great explanation and easy to understand steps!

[@fireflylectures]

Hi Clary, no it is correct. The formula for a plane is a(x-x0) + b(y-y0) + c(z-z0) = 0. So with the first term 4(x+2), the a=4 and the x0 = -2 since it has x+2 which equals x - (-2). Hope that helps. :)

[@fireflylectures]

Lieth Wahid That's correct. In the equation of a plane, you have a(x-x0)+b(y-y0)+c(z-z0)=0. So, you have to account for the minus sign when determining x0, y0, and z0. E.g. (x-2) would mean x0=2 as you said. For (y+5), y0 would equal -5. For (z-8), z0 would equal 8.

[@noahgsolomon]

Best. teacher. ever!

[@hafsaimtiaz5832]

From where does uh get value of 'P' and normal 'n' ??...plz clear my doubt

[@Noname98283]

normal n comes from coeffs of the equation, i dont know where p comes from

[@visas2226]

Brief and useful, i really enjoyed it. 🙂🙏

[@SosoKoko21]

This is very useful, thanks a lot :)

[@CocoaThunda]

how do you decompose the plane formula in standard form to your point "p" and and the normal vector "n"?

[@dreamurlife]

Hi great video! But Is P meant to be (2, -5, 0) instead of negative 2?

[@aghaabbas6845]

Clary L a (x-x0) 4 (x-(-2)) so -ve 2

[@crochetyoustay]

How do you find the distance if only a point Q and the Cartesian equation of the plane are given? I just subbed in random values into the equation to find a point P, but I can only find the magnitude of vector PQ and have no other information, no way of finding a point N or vector n

[@garethm3171]

Please could you explain how you get P = (-2 , -5, 0) . thanks.

[@hafsaimtiaz5832]

@iHelper Pro thnks man..

[@aghaabbas6845]

very helpful. thanks!!

[@fabiannghitewapo2424]

Shouldn't we get the magnitude of the dot product (5)?

[@pawelsliwa6191]

wish you did more than 1 just example

[@DrBwts]

how do I get the coordinates of D?

[@nemathassnain8522]

Thank you!

[@brcarter1111]

Way easier to just sub coordinates of point P(x1,y1,z1) into cartesian equation / n of cartesian equation. |Ax1+By1+Cz1+D| d= ______________________ √(A^2 +B^2+C^2)

[@jackssweetnothings9974]

Bro you just saved my ass, thank you

[@mochelevy7081]

nice vid but 21 isnt a prime number

[@fireflylectures]

Moché Levy yes you are correct, I misspoke. I meant it doesn't have any factors which are perfect squares, which would have allowed the radical term to simplify.

[@davidrheault7896]

@@fireflylectures but 21 is square free, maybe that is what you meant. the mobius of 21 is +1

[@young5126]

THANK YOOOOOOU