Calculating Perpendicular Point on a Line in 2D Plane

  • Thread starter Thread starter Asuralm
  • Start date Start date
  • Tags Tags
    Point
AI Thread Summary
To calculate the point C that makes AC perpendicular to BC on a line L in a 2D plane, the relationship involves substituting C into the equation and ensuring the inner product <AC, BC> equals zero. The vectors AC and BC can be expressed in terms of the line's parameters and points A and B. The inner product simplifies to an expression involving the dot products of these vectors, but without specific values for A, B, v0, and n, further simplification is challenging. The discussion highlights the complexity of deriving a more straightforward solution without concrete data. Ultimately, the mathematical relationship remains intricate and requires specific inputs for resolution.
Asuralm
Messages
35
Reaction score
0
Hi all:

Given a line L:v= v0+t*n; and two points A, B in 2D plane; A and B are on the two sides of the line L. I want to calculate the point C which makes AC is perpendicular to BC

I know it's simply that substitude v to C and <AC, BC>=0. But I don't know how to simplify the equation.

Could anyone help me please?

Thanks
 
Mathematics news on Phys.org
Asuralm said:
Hi all:

Given a line L:v= v0+t*n; and two points A, B in 2D plane; A and B are on the two sides of the line L. I want to calculate the point C which makes AC is perpendicular to BC
C is on L?

I know it's simply that substitude v to C and <AC, BC>=0. But I don't know how to simplify the equation.

Could anyone help me please?

Thanks
The vector AC= v0+ t*n is given by v0+ t*n-A. The vector BC is given by v0+ t*n- B.
Their inner product <AC,BC>= <v0+ t*n- A,v0+ t*n- B>= |v0- t*n|2- <v0+ t*n,A+B>+ <A,B>.
Without specific values for A and B, v0 and n, I don't see how you can get any simpler than that.
 
should this |v0- t*n|2- <v0+ t*n,A+B>+ <A,B>

be <v0+t*n, v0+t*n> - <v0+t*n, A+B> + <A, B> ?
 

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 '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 '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

B A triangle problem: Prove that |AC|+|AB|=|PR|+|PQ| given some constraints
Replies
13
Views
2K
B Reprise: Calculate the distance between two points without using a coordinate system
Replies
1
Views
2K
I Two vectors and two perpendicular lines
Replies
20
Views
2K
I Are there any two pairs of integers with the same result in a specific function?
Replies
7
Views
2K
I Expressing any given point on plane with one unique number
Replies
4
Views
2K
MHB Proof Quest: Non-Equilateral Triangle Enclosing Point Z
Replies
3
Views
2K
I How can you represent a point by "z = x + iy" as shown here?
Replies
10
Views
2K
B How to calculate a perpendicular line?
Replies
11
Views
3K
I Fınding the position of a point on the line
Replies
1
Views
1K
I Closest point on a plane to a point near the plane
Replies
6
Views
3K

Hot Threads

Recent Insights

Back
Top