# 3D vectors

Printable View

• Feb 11th 2013, 06:27 PM
romean2015
3D vectors
Given points A and B in 3-dimensional space, describe the solutions to
−→ −→
P A • P B = 0.
• Feb 11th 2013, 09:00 PM
Soroban
Re: 3D vectors
Hello, romean2015!

Quote:

$\displaystyle \text{Given points }A\text{ and }B\text{ in 3-space, describe the solutions to: }\overrightarrow{PA}\cdot\overrightarrow{PB}=0$

Consider a sphere with $\displaystyle AB$ as its diameter.
Consider any point $\displaystyle P$ on this sphere.
Draw chords $\displaystyle PA$ and $\displaystyle PB.$
Code:

              * * *           *          *  P         *              o       *                *       *                  *     A o - - - - * - - - - o B       *                  *       *                *         *              *           *          *               * * *
$\displaystyle \text{Since }\angle APB = 90^o,\,\text{ then: }\,\overrightarrow{PA}\cdot\overrightarrow{PB} \,=\,0$

$\displaystyle \text{Therefore, the locus of point }P\text{ is the sphere with diameter }AB.$