# Thread: 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 $\displaystyle P$ and $\displaystyle Q.$
i need to find point $\displaystyle R$, defined by the intersection of $\displaystyle \overrightarrow{PR}$ and $\displaystyle \overrightarrow{QR}.$

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

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

We have a semicircle with diameter $\displaystyle PQ.$

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

Then: .$\displaystyle PR \perp QR$

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 $\displaystyle PQ.$

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

Then: .$\displaystyle PR \perp QR$