Can area of a triangle be 0.5(c x a) instead of 0.5(a x c)?

  • Thread starter Thread starter coconut62
  • Start date Start date
  • Tags Tags
    Area Triangle
AI Thread Summary
The area of a triangle can be expressed as 0.5 times the magnitude of the cross-product of two vectors, represented as (1/2)||A x C|| or (1/2)||C x A||. The direction of the vectors does not affect the area calculation since both expressions yield the same magnitude. This relationship holds true regardless of the angle between the vectors, provided angle B is not specifically 90 degrees. The discussion clarifies that the right-hand rule and vector directions are not relevant to the area calculation itself. Overall, the area formula remains consistent across different vector arrangements.
coconut62
Messages
161
Reaction score
1
Please see the image attached.

Does that have anything to do with directions? The right-hand rule?
 

Attachments

  • 993936_10151648940262830_1434348128_n.jpg
    993936_10151648940262830_1434348128_n.jpg
    23.4 KB · Views: 519
Mathematics news on Phys.org
ca = ac, so yes.
 
Not in that figure, unless angle B is 90 degrees.
 
using the magnitude of the cross-product of two vectors to find the ar

If you mean

Area of triangle = (1/2)||A x C|| = (1/2)||C x A||

as in, using the magnitude of the cross-product of two vectors to find the area of the triangle between them, then yes.
 

Attachments

  • area.png
    area.png
    369 bytes · Views: 400
mark.watson said:
If you mean

Area of triangle = (1/2)||A x C|| = (1/2)||C x A||

as in, using the magnitude of the cross-product of two vectors to find the area of the triangle between them, then yes.

I didn't see the second part of your question. The direction of ||A x C|| or ||C x A|| doesn't matter because they have the same magnitude. That is why (1/2)||A x C|| = (1/2)||C x A|| is true.
 
Thank you very much.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

I Help with area formula using direction cosines
Replies
3
Views
2K
B Find triangles with areas that are integers
Replies
20
Views
3K
MHB Area of Triangle ABC: Find the Answer Here
Replies
2
Views
1K
MHB Find the areas of segment in circle
Replies
1
Views
2K
Finding area of a non right angled triangle
Replies
9
Views
3K
MHB Calculate Area of Triangle ABC
Replies
2
Views
5K
MHB The area of a triangle and determinants
Replies
1
Views
2K
MHB Ratio of the area of triangle in terms of another triangle
Replies
6
Views
2K
MHB Why Can't a Right Triangle Have Sides that Add Up to the Area of Squares?
Replies
2
Views
2K
MHB What is the area of an isosceles triangle with side lengths 6, 6, and 4?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top