Distance between a point and a plane (vectors) (KristaKingMath)

Learn how to find the distance between a point and a plane. Use the distance formula for the component of b along n, where b is the vector between a point in the plane and the given coordinate point, and where n is the normal vector to the plane. The distance formula takes the dot product of the normal vector and the vector b, but simplifies to a formula that simply pulls the components from the coordinate point, and the coefficients from the equation of the plane.

● ● ● GET EXTRA HELP ● ● ●

● ● ● CONNECT WITH KRISTA ● ● ●

Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[muneeralibrahim]

Thank you very much
you ended an era of confusion, this became one of the easy sections. 

[easonxu]

Even its 2020 and the video is years ago, it really helps me a lot!!! This is way more beneficial than my lectures, thank you so much!!!

[ayandamtshabe]

you are doing great job, you save us from pain of failure. l understand most of the staff through your lesson.

[malleharana]

Thank you so much! Your videos are the only reason why I do well in math. Keep making wonderful videos! You are a life saver!

[toddsecor]

WOW! This is so much easier than using my instructor's method. Thanks!

[JAY-qpfi]

Best lecture I found on this
Thanks ❤😊

[codingwithelhacen]

Beautiful explanation. it's always satisfying to watch your educational videos.

[adaturanli]

i'm preparing for an exam that is full of topics I don't know, and your videos help so much every time. thank you so much and i love you. I'm sure a lot of people will agree with this hahah

[osmfacts]

Thankyou very very much cuz I had been confused for long time about the "d" .
How to put d ..
with negative sigh or without?

[Uzamakifan]

good video. I'm currently in calc 2 and this concept came up, my prof taught the idea using only projections and dot product over magnitude (i.e first equation), but he kept on mentioning (w/ disgust) that the author of our course textbook chose to instead use the " big, unnecessary, ugly formula" instead of providing a method solely using the 'fundamentals'. I was simply curious as to what this 'ugly formula looked like (its not bad).
One critique though: you didn't have to go through that extensive process as to why 'd' was negative... simply saying to set the plane equation in standard form would suffice. Also, I would've like to see you work out how the numerator of the first equation (n dot b) equals the numerator of the second. Overall great video! Keep up the good work!

[midsummerstation]

great video but how did you come up with this formula that's what i wanna know

[alyamarini]

omgg ur way is wayyyy shorter than mine thankiu so much ! very helpful 👍👍👍

[danxdaniel]

This is so usefull, your videos are going to help me pass an exam !

[arslna]

Thank you, I have exam in next 30min, and U saved my liiife ...

[nancyndaruga]

how do you find b according to your explanation at the beginning of the video

[jeraldalbao]

i still need to find a point on the plane and get the coefficients of the vector it forms with the point right? That would be my vector "b" which is to be dotted with the vector normal to the plane...

[Diegownz]

so much easier than the projection method

[nolanbannon]

why does (n)dot(b) equal 18 and the point (p)dot(n) also equal 0? (b) and (p) are very different, one being a point, and one being a subtraction of (p) from any point on the plane?

[rawrtid]

finally an explanation i understand (: thanks

[donyajohari]

how do we go about finding the point on the plane where one end is the point outside the plane and the other one is one the plane?