Calculating Perpendicular Point on a Line in 2D Plane

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The discussion focuses on calculating the perpendicular point C on a line L defined by the equation v = v0 + t*n, given two points A and B in a 2D plane. The goal is to find point C such that the vectors AC and BC are perpendicular, which is mathematically expressed as = 0. Participants provide insights into the vector representations of AC and BC, leading to the inner product equation |v0 - t*n|² - + . Simplification of this equation is challenged without specific values for A, B, v0, and n.

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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
 
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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> ?
 

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