Distance between planes | Vectors and spaces | Linear Algebra | Khan Academy

2010 IIT JEE Paper 1 Problem 51 Distance Between Planes

Missed the previous lesson?

Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

[ばにゃにー]

Just finished all 144 videos and I wanted to thank you for teaching me. It was definitely interesting, and I'll be looking forward to any future videos.

[anuragmishra]

I am an IIT JEE 2020 aspirant. Your videos have helped me a lot.
Thank You.

[fashionvella]

Finally finished the whole linear algebra playlist. Math is not my major but just because of khan's way of explaining math I fell in love with math. The way you teach I have never learned this way in my whole life. I was just solving questions by remembering formulas, but you changed my whole perspective for math. Now going to learn calculus from your amazing lectures.
Thank you much Sal
😍😍😍😭

[goclbert]

If anyone is wondering where to go now that you've finished the playlist, I'd recommend looking up the MIT 18.06 course on linear algebra. Try to do the first two quizzes and if you have any trouble, watch the corresponding MIT lecture videos. Once you feel comfortable with those, finish out the rest of their linear algebra lectures and try the final exam and quiz.

[markeppard]

Perhaps someone could clarify this... Starting at 11:08 Sal keeps saying "lets find the distance between the two planes" and continues looking for "the distance" for the remainder of the video.

I'm confused because it gives this distance in the initial problem. After reading the questions and comments, everyone else seems equally confused, and none of their explanations are correct either.


Isn't this the same as the distance in this situation since the d-value of the blue plane in the equation is 0 in the equation
-x +2y -z=0 (before he multiplies both sides by -1)?

Since the equation of the blue plane in this video is found to be -x +2y -z=0 (before he multiplies both sides by -1), it makes sense that the equation for the red plane can be written as x -2y +z = 6, since it's a distance of 6 units up from the blue plane, however, it contradicts with the given distance of square root (6), which is approx. 2.45.

Since the planes are parallel, doesn't the distance between them remain constant?

What is the actual distance?

[Elmaxsivu]

Finished 144 videos... MY brain hurts, but I would like to thank you a lot.

[bikashthapa]

finally i have completed whole playlist

[mister]

It was a long ride but I finally made it to the end! Thanks for these awesome Algebra videos!

[alinapostol]

Just completed the playlist. Thank you for everything Sal!

[redteamdarkspear]

I just got to the symmetric equations in my calculus tonight. I know they're not actual calculus equations but I'm glad to see that they're used in other subjects as well

[lhyx]

is it the last video for linear algebra? can't believe i finished the course within 2 weeks.

[loganmanuel-mcgarry]

just to clarify: he is solving for ‘d’ in the equation of the first plane, right? because distance is given, but the ‘d’ value of the first is not.

[Evdis]

From the bottom of my heart and my now very tired brain: THANK YOU for this playlist.

[kcwilliamson]

Will Wei is right and Arnav Barbaad is wrong. The denominators are the components of the direction vectors for the lines, not the position vectors for a plane. Sal could have just used them instead of working so hard.

[willwei]

Can't you just cross (2, 3, 4) and (3, 4, 5) without finding random vectors using points like a = 2i + 3j + 4k and b = i + j + k

Wouldn't that get you the normal of the plane as well?

[yangyuew]

I think he meant the distance between the two closest points should be sqrt(6) at the end of the video

[coachlebron]

Just a suggestion Sal. Could it be at all possible that you include in the description or as links the related videos you talk about. When you mention them in videos they arent always easy to find. Only if its not too much trouble

[wanx]

when Khan did this, to find vector N * the other part=0, can I use a different vetor(maybe(2, 3, 4)) to also be =0 and slove it?

[greedskith]

SAME QN IN WBJEE 2023 WAS JUST SOLVING IT AND GOT STUCK, 😄

[leadtoexemplify]

To find the distance all you need is a point and the plane equation. You found the point already at the beginning. I don't understand the need to figure out equation of another plane. of course it proved that plane containing other two lines is parallel to the plane in question. Did I miss something?