# orthogonal vectors point of intersection

• Dec 23rd 2009, 09:24 AM
thesys
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
• Dec 23rd 2009, 10:32 AM
Soroban
Hello, thesys!

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

Quote:

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: .$\displaystyle PR \perp QR$

• Dec 23rd 2009, 10:55 AM
thesys
Quote:

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: .$\displaystyle PR \perp QR$