Area of Triangle with three vertices using Vector Cross Product in 3D Coordinate Plane

Area of Polygon: • Boxing-in and Shoestri...
Cross Product Playlist: • Vector Dot Cross Produ...
Area of triangle is half the area of the parallelogram. Area pf parallelogram is the magnitude of cross product of adjacent sides.

[@DragonLoad49]

i was looking for a different way to do this type of problem, but this is a very well explained example of the baaic technique. Why would anyone dislike this?! You are a great teacher sir! If I had not understood this method before, surely now I would. Wonderful video!!

[@MathematicsTutor]

Thanks a lot for appreciation.
Don't look at the 11 dislikes; There are 96 likes also.
Many of our viewers do not understand the concept of cross product and so we can't blame them!
Felt like sharing with you. Thanks

[@ziggymarley6145]

2:34 the method you used to write the cross product is an exceptional time saver.
I used to write it out in a matrix form and cross each individually, leading to many mistakes. Thank you for this.

[@MathematicsTutor]

That is so true.
I still use both the methods as the matrix is commonly applied in many places.
Thanks for appreciation

[@MathematicsTutor]

Cross Product Method 2: ruclips.net/video/4LKZw2_SUpA/видео.html

[@3rdSalimo]

i am the perfect example of what you would call a lazy student. i didn't know how to solve such eqautions yet i have an exam tomorrow. this video helped me. thanks..

[@MathematicsTutor]

Thanks for appreciation. All the best.

[@reetichauhan355]

Sir when just the components of three sides are given, how do you know which two sides to vectorly multiply out of given three ?

[@wessionaldo6853]

One side is always fixed

[@KeshavPatel-ux5cx]

Golden days when youtube was used for giving information rather than just views😢

[@mr2seis388]

I don't understand. The question was asking for the area of a triangle yet you found the area of the parallelogram. Is it because we should divide the parallelogram answer by half to get the area of the triangle?

[@Crafter4032]

He did find the area of a triangle as he did say ...the area of a triangle is half the area of a parallelogram 😅...

[@angellicat.n.g2382]

k(-4+1). -1 x -1= 1. Right?

[@prajwalsah7595]

Sincerely I would like to Thank you SIR...THANK YOU

[@MathematicsTutor]

Thanks a Lot!
That provides me with the energy to do something better and share my passion. Thank you!

[@reetichauhan355]

When we are finding AB vector, why do we subtract B components - A components? Shouldn’t it be A-B?

[@andrewguan1598]

it doesnt matter which ones but the other vector has to be the same way, whether it be b-a or a-b, the other one has to subtract the same way

[@tsynabrachris2358]

I want to help me with this one....... The points A(1,2,3) , B(3,3,5) and C (3,0,5) form a triangle. Calculate the area of the triangle

[@MathematicsTutor]

Let me know in the concept of cross product is known to you or not. I may share an alternate approach. Meanwhile check this playlist. ruclips.net/video/cbVAyCS3AN0/видео.html
Hope that helps. Thanks

[@MathematicsTutor]

Here is a playlist that can help you to find the solution. PLAYLIST: ruclips.net/video/cbVAyCS3AN0/видео.html
Also let me know if you understand vectors. If not, I will upload the solution with different approach. Thanks

[@brenn7754]

Doesn't the j component of the cross product have to be positive because when you take the determinant, the sequence alternates in a sign?
|+ - +|
|- + - |
|+ - +|
x = xj +4j - 5k

[@kiplangathezron783]

You're right +-+

[@semiqerelevu]

iX-jY+kZ

[@sayedhamrazhaider869]

Thanks You Sir this vedio is very helpful🥰🥰

[@ghanajieha3785]

sorry sir may i ask where did u got the -1,2,2,-1 and -2,1,-1,-2 from? i just didnt understand that part only. TQ

[@MathematicsTutor]

That is the cross multiplication of vectors AB and AC. You can yous your matrix method to do so. Hope that is clear. Thanks

[@alphasauroxviix4235]

love it, very clear and concise explanation

[@RottingFarmsTV]

You are a lifesaver, amazing!

[@rakharahmadikaputra9207]

Thank you very much this video really help me finishing my quiz

[@morby.vinas0476]

Thank you so muucchh❤️❤️

[@danielwang4917]

Thanks, Anil! Great explanation

[@akashagrawal7609]

The question is...
Is it allowed to take the cross product of cb and ac or cb and ab?

[@MathematicsTutor]

Both cross products will give the same result. Try it out.
Thanks

[@akashagrawal7609]

Anil Kumar thanks sir.

[@ayeshahameed9583]

It helps alot tysm!

[@MathematicsTutor]

Thanks. Here is related Playlist: ruclips.net/p/PLJ-ma5dJyAqqrUTZTjZzozQ6jnzNiiwkV

[@sampathvillagedancer9380]

Very clear sir tqqq so much......👏

[@manishpoudel5220]

okay but vector j while doing cross product in the middle must be negative isn't it ?

[@MathematicsTutor]

There are different ways of finding the cross product. When Matrix is used then we make it negative for vector j. Try with your method and compare the answers, Hope that helps.

[@comrade.bonifaceonoyima416]

Translate a triangle with vertices at original coordinates (15, 30), (10, 15), (25, 15) by tx = 20, ty = 10. Roughly plot the original and resultant triangles.

[@claricea5353]

very helpful, thanks!

[@davidpaul576]

Sir it was very useful

[@gp873]

What about if the problem were to say the triangle was in R3?

[@MathematicsTutor]

The triangle is in R3 since all the three coordinates are given for the vertices. Thanks

[@gp873]

@@MathematicsTutor oh I see. So it doesn’t change the way you would solve it like you did here?

[@thebayliefactory5252]

Thank you!!

[@dievereybagatsolon6433]

you saved my life

[@MrSidTaylor]

The statement that the area of a parallelogram is the magnitude of the cross product of adjacent sides is an assertion which I have never seen proved.

[@ticktick2650]

Thank you sir

[@braidenfernando8931]

how come you dont find CA and cross it with CB?

[@MathematicsTutor]

You will get the same result with CA x CB
Thanks

[@luminamathavan8894]

Why AB x AC? Why not AC x AB??

[@MathematicsTutor]

For Area you could do AC x AB also since we are interested in the absolute value.
Thanks

[@luminamathavan8894]

Sir, I want to prove Area of Parallelogram from Area of Triangle. So it matters, isn't it??

[@farajadelaja]

thank you sir!

[@feaarisa321]

Sir, How do you calculate the final answer..cuz the answer i get is 3.535...i dont get 59 units

[@hawks5352]

that doesnt say 59 units it says sq. units as in square units

[@sylvesterouma7662]

very helpful

[@MathematicsTutor]

Here is related Playlist: ruclips.net/p/PLJ-ma5dJyAqqrUTZTjZzozQ6jnzNiiwkV
Thanks

[@nyimathinley9978]

Thank you

[@mdgulamgaush5595]

I personally feel very bad ☹️ why people dislike.if can't like something then they are not supposed to dislike some one.this shows bad nature of student. If you have problem,just try to put your problems with out feeling problem in someone

[@MathematicsTutor]

I think The comment below by Daniel explains the truth. Finding area of triangle with cross product vector application is not a popular method. Unfortunately, this important method is overlooked.
Here is another good application of this method. ruclips.net/video/1qt9euzibNY/видео.html
Thanks

[@yashikyashi5580]

Thanks

[@awais_hanzala81]

Sir very simpal 🥰🥰🥰

[@qs3946]

thanks, help a lot

[@hermanmontvelisky3162]

Right triangle and answer but seems to me you ended up using the wrong parallelogram.

[@dennismumo9877]

Correction its supposed to be (-2 -1 1 -2) its -1 before 1

[@ayeshahameed9583]

Wot bout unit? I didn't get it

[@MathematicsTutor]

square units for the units of area.

[@MathematicsTutor]

Thanks

[@legendfacts9174]

But after all nice sir keep it up

[@yusufkhan1193]

I like this video

[@CR-bu3sy]

Thanks sir

[@MathematicsTutor]

Thanks. Here is related playlist: ruclips.net/p/PLJ-ma5dJyAqqrUTZTjZzozQ6jnzNiiwkV

[@JawadAli-tj3ec]

Thank u

[@power5able]

thank youu

[@sampulchyrmang4660]

🥰🥰🥰🥰🥰🥰🥰

[@doomddudc6440]

Hmmm interesting

[@bhavyarora3893]

J cap will be negative

[@MathematicsTutor]

Calculations are correct. Let me know the step which is not clear. Thanks

[@fiszam9339]

sir i think it will become (-4+1) because - and - it will become positive, at 3:35

[@morby.vinas0476]

The formula is (-4 - (1)) thus making it still (-4-1)

[@KOBE2224MVP]

i think it should be - j(-2-2)

[@MathematicsTutor]

You could have -j(2 + 2). That is same as j(-2 - 2)

[@MathematicsTutor]

You probably use matrix method as shown in this example: ruclips.net/video/4LKZw2_SUpA/видео.html

[@chriscozilas]

your a fucking gangster

[@mohitthakur_7674]

Wrong answer bta rhe ho

[@MathematicsTutor]

Answer is correct. Thanks

[@legendfacts9174]

According to me this is not useful to everyone

[@paulkta8635]

Thank you

[@brendakerubo97]

Thank you sir

[@nomthethomaseko1833]

thank you