# Math Help - orthogonal vectors point of intersection

1. ## orthogonal vectors point of intersection

Hello,

Hello,
I have two points p and q. i need to find point r which is defined by the intersection of the vectors pr and rq. the vectors are orthogonal, so that <pr,qr> = 0

how can i get the point r ? How can I define my lines so i can make pl1 = ql2

2. Hello, thesys!

If I understand the problem, there is an infinite number of answers.

I have two points $P$ and $Q.$
i need to find point $R$, defined by the intersection of $\overrightarrow{PR}$ and $\overrightarrow{QR}.$

The vectors are orthogonal, so that: . $\overrightarrow{PR}\cdot\overrightarrow{QR} \:=\:0$

How can i get the point $R$ ?
Code:
* * *     R
*           o
*          *    *
*       *         *
*
*  *                *
P o - - - - * - - - - o Q

We have a semicircle with diameter $PQ.$

Let $R$ be any point on the semicircle.
Draw chords $PR$ and $QR.$

Then: . $PR \perp QR$

3. Originally Posted by Soroban
Hello, thesys!

If I understand the problem, there is an infinite number of answers.

Code:
* * *     R
*           o
*          *    *
*       *         *
*
*  *                *
P o - - - - * - - - - o Q

We have a semicircle with diameter $PQ.$

Let $R$ be any point on the semicircle.
Draw chords $PR$ and $QR.$

Then: . $PR \perp QR$

I mean that the points are like this:
*r------*p------- |
|
|
*q

4. Yes, I am sure Soroban understood what "orthogonal" meant!

And his answer is still true. Take any line through point p, except for the single line through both p and h, and there exists a line through q perpendicular to that line. There are an infinite number of possible lines through p and so an infinite number of points "r" at which lines (vectors) through p and q are orthogonal.