Other sandboxes: Main sandbox | Template sandbox
T h e C a r t e s i a n p r o d u c t $ R × R × R = { ( x , y , z ) ∣ x , y , z ∈ R } $ i s t h e s e t o f a l l o r d e r e d t r i p l e s o f r e a l n u m b e r s a n d i s d e n o t e d b y $ R 3 $ . W e h a v e g i v e n a o n e − t o − o n e c o r r e s p o n d e n c e b e t w e e n p o i n t s $ P $ i n s p a c e a n d o r d e r e d t r i p l e s $ ( a , b , c ) $ i n $ R 3 . $ I t i s c a l l e d a t h r e e d i m e n s i o n a l r e c t a n g u l a r c o o r d i n a t e s y s t e m . N o t i c e t h a t , i n t e r m s o f c o o r d i n a t e s , t h e f i r s t o c t a n t c a n b e d e s c r i b e d a s t h e s e t o f p o i n t s w h o s e c o o r d i n a t e s a r e a l l p o s i t i v e . {\displaystyle TheCartesianproduct\$\mathbb {R} \times \mathbb {R} \times \mathbb {R} =\{(x,y,z)\mid x,y,z\in \mathbb {R} \}\$isthesetofallorderedtriplesofrealnumbersandisdenotedby\$\mathbb {R} ^{3}\$.Wehavegivenaone-to-onecorrespondencebetweenpoints\$P\$inspaceandorderedtriples\$(a,b,c)\$in\$\mathbb {R} ^{3}.\$Itiscalledathreedimensionalrectangularcoordinatesystem.Noticethat,intermsofcoordinates,thefirstoctantcanbedescribedasthesetofpointswhosecoordinatesareallpositive.}
