Given points A and B in 3-dimensional space, describe the solutions to
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P A • P B = 0.
Hello, romean2015!
$\displaystyle \text{Given points }A\text{ and }B\text{ in 3-space, describe the solutions to: }\overrightarrow{PA}\cdot\overrightarrow{PB}=0$
Consider a sphere with $\displaystyle AB$ as its diameter.
Consider any point $\displaystyle P$ on this sphere.
Draw chords $\displaystyle PA$ and $\displaystyle PB.$
$\displaystyle \text{Since }\angle APB = 90^o,\,\text{ then: }\,\overrightarrow{PA}\cdot\overrightarrow{PB} \,=\,0$Code:* * * * * P * o * * * * A o - - - - * - - - - o B * * * * * * * * * * *
$\displaystyle \text{Therefore, the locus of point }P\text{ is the sphere with diameter }AB.$