Area of Triangle Formed by Two Vectors using Cross Product
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- Опубликовано: 25 авг 2024
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Area of Triangle Formed by Two Vectors using Cross Product.
Here we find the area of a triangle formed by two vectors by finding the magnitude of the cross product.
subscribing is a good thing! :)
Lol
Patrick, you really are the best. I've watched many of your videos and yours are the most helpful I've seen on RUclips. Thank you
why is a cross b the area of the parallelogram though explain please
Area of parallelogram= absin(theta)
ā x b = absin(theta)
Hence, ā x b = area of parallelogram
Thank you so much, within less than a minute you answered a question to which i had spent hours searching for a answer!!
+Nathaniel Blakely awesome! glad i could help!
Nice video sir. Explained beautifully❤
Helped me to find out area of triangle easily.... Thanks!! 👍👍
I just subscribed yesterday and the very first video you upload, boom its what i'm studying for my test tomorrow. You the man!
Very helpful, i have been spending the past hour looking for a way to use the cross product equation to find the area of a triangle given 3 3-D points. But got stuck when i ended up with a vector, and wasn't sure if i was allowed to just take the magnitude of that vector. Although you didn't touch on that specifically it did help to confirm my suspicions :D
Right now on to question 2 of 12.... darn.
P.S If you do happen to read this can you explain what the n(circumflex or hat) is in the equation AxB=/A//B/sin(a)n^
I prefer this method also. However, since the determinant could be negative, we need to take half of the ABSOLUTE VALUE of the determinant. The geometric interpretation of a negative determinant is the transformation of the unit vectors into the two vectors which form two sides of the triangles were reflected across a line, (i.e. the i vector is above the j vector.)
damn Patrick, you're an artist
There is also a pretty neat trick/calc promulgated by the wizard Gilbert Strang. Given points a,b, and c you get the area by taking the determinant of the three points taken as row vectors with an extra column of 1's and then dividing by 2. Think about how much time this might save you on the ACT. For example if the points are (0,0), (2,0) and (1,1) you do something like the
det | 0 0 1|
| 2 0 1|
| 1 1 1|
how are these related to what you are doing here?
love your videos so much they are really helpful, just wanted to point out that you said 0-4 is 0 i think you meant to say 0 multiply by 4 is 0?
Omg. This was so easy but I didn’t know how to do it because it wasn’t covered in lecture and the online homework never asked.
I hate when professors quiz you on things not covered but I’m more mad at myself for not thoroughly covering the chapter.
Thank you!
You're a wizard and for that I thank you
Thank you bro❤️
Thank you
Thank a lot tomorrow is my exam this helped a lot.
Amazing video!! Thank you so much
It i interesting to know why magnitude is equal to magnitude of resultant vector. I can follow these calculations but don't understand why it gives area.
thank u so much for uploading this video. it was so helpful
Thankyouuu !
Wow, if that's true, that would save an AMAZING amount of time. I actually got to meet Gilbert Strang - he really is a genius.
2:11 "zero minus 4 is 0" did you mean multiply?
Yes he did, just for anyone watching this now.
Matthew Sbar thank u lol
Yes it means to multiply
a few years late but yea he meant multiply
Machannee ❤️ nee polichh
You, sir, are brilliant. Thank you so much!
Hi Great video , just one mistake but when you simplify the square you forgot about the two before tanking out the 3^2 answer should be (6xsqrt(6))/2
6 times sqrt(6) divided by 2 equals 3 times sqrt(6). In other words, you got the same answer as patrick, but you didn't cancel out the 2 on the bottom which he does at about 4:37, his answer is more simplified but they're both the same quantity.
Patrick, u r the best!
Very well explained, thank you very much!
Howdy, Patrick, let me ask you a question. As a math whiz, what do you think of Christopher Langan and his CTMU? Supposedly, he's smarter than Einstein and is working on a theory that will revolutionize science and change the world forever. He thinks he is closer to absolute truth than any man before him and he is certain that his theory will help prove the existence of "God". What do you think of all that?
do you have a playlist for just Calc 3 (multivariate) ? i couldn't find this video on your website
Why do you subtract the j component, not add????
Is there any trick to make sure we. Have the right answer?
Thanks again, man!
Just looked it up, on wiki it says Radical comes from the latin radicalis "of roots" and from Latin radix "root". So I guess so never heard of it before though
At 2:12, you say 0 - 4 is 0, doesn't that skew the results? The i component of the cross product should be -4 - (-6) = -4 + 6 = 2, not 6, right?
I wish you were my calc 3 professor
youre so awesome thanks for the video
this is awesome !!!! thanks
good one
why we only using Cross Product. please give a reason for it.
Thank you!!
how to solve when we r given with only 2 components ??
Saurabh S Gowda you call it a triangle?
Take third component as 0
Why is the area of the parallelogram the |axb| ?
thanks
it is helpful... thenks
low tech but well done
i can add some star wipes if that makes the math better
What's the difference between dot product and cross product?
to start with: a dot product is a scalar (a number) whereas a cross product produces another vector
You can also use dot product to find the area :D
Bro I think that the part of cross product having î vector is calculated wrong......plz confirm....the multiplication of that part is wrong
how did you get a positive 6i?
+Brian Coughlan Under the assumption you mean the coefficient of the i-component it is due to the way you find the determinant ---> (0*4)-(1*-6)=6
Rather than 6(-1)^0.5 that is :P
for j: j = k X i
Thus, you get the negative if you do i X k as he does in the video.
That's bad ass (Y) :D
Neatest left hander i know
YOU MEAN ITS POSITIVE 6 NOT -6
kind of wish the whole solution was displayed
its a cross product so 0 TIMES -4 is 0.
haha I'm an idiot, thanks
боже я же все это должна была за все 14 недель выучить,а не ночью перед экзаменом
Thank you
Thank you!