Vector triangle inequality | Vectors and spaces | Linear Algebra | Khan Academy

Proving the triangle inequality for vectors in Rn

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[The.Ghost.of.Tom.Joad.]

Thanks Sal. You are a great teacher. Twenty or so years ago, the Cauchy-Schwarz and Triangle inequalities baffled me. I never understood them--just parroted some worked examples I had.

Compare.
->You: I listen and jot some things down for 25 minutes. My understanding, solid. I pulled out an old LA book, and ripped off a few problems correctly. No need to look @ the solved problems.
->OSU ~1990: 3 lecture, 5 recitation and over 10 study hours. Baffled. Had to memorize algorithms.

Thanks

[annerigouws]

How can I use this result ||x + y|| <= ||x|| + ||y|| to prove the inequality ||p - r|| <= ||p - q|| + ||q - r||?

[hafsamariyam]

That could be a great video if some corrections were made.

1. In the first step, that is, length squared of x+y doesn't equal the dot product of vector with itself; dot product should be replaced with sum of the vectors.

[Liaomiao]

lol @ nerd rage in the comments, kinda lightens the mood from all this concentration

[futterkulcha]

Visual representation of inequality + triangle and straight line case = mind blown

[JaspreetSingh-zpnm]

Sal, What argument would you use to prove triangle inequality for vectors that are not colinear? Or when y is not some scalar multiple of x.

[panickingkiwi]

11 years later, still of great help. Thank you hahahah.

[PhysicsMath]

Prove vectorially that the opposite side of parallelogram are equal and diagonals bisect each other

[LAnonHubbard]

This was really helpful to see what the previous video was meaning. Thanks.

[souravmallick]

Just here after 11 year's to solve my present problem 😶

[regingwapo]

I think it would be more insightful if you provide a geometric interpretation of x=cy at 14:50

[eileenBrain]

@Hefotos ok apart from triangle inequality, but still not enough examples and explanations in 3d space. it would be better if the tutorials were more about 3d space oriented and not algebra equation solving and simplifying something that is simple enough.

[boomit]

He prolly wasn't gonna pass the test anyway, hence even this explanation was too hard for him to comprehend :D

[eileenBrain]

Ok so i guess the audience is him himself! Otherwise why would anyone waste their time watching this crap when they can simply look things in some book?! Which would be better and quicker. Thought this stuff was for beginners, but this guy goes on about some meaningless examples like two vectors and solves meaningless equations with them. So my point is, if you want to apply this to a meaningful example with a 3d graphics api then you are left with nothing helpful at this moment.