Math Question and Answers


Question and Answers Forum

All Questions Topic List
Geometry Questions
Previous in All Question Next in All Question
Previous in Geometry Next in Geometry
Question Number 210761 by mr W last updated on 18/Aug/24

Commented by mr W last updated on 18/Aug/24

$f i n d t h e r a d i u s R o f t h e l a r g e s t s p h e r e$ $w h i c h c a n b e p l a c e d b e t w e e n t h e r e d$ $a n d b l u e p l a n e s i n t h e f i r s t o c t a n t .$ $a s s u m e 0 < p ⩽ a, 0 < q ⩽ b, 0 < r ⩽ c .$
Commented by mahdipoor last updated on 18/Aug/24

$p l a n e s i s n o t i n f i n i t y ?$
Commented by mr W last updated on 18/Aug/24

$t h e s p h e r e m u s t c o m p l e t e l y l i e i n$ $t h e f i r s t o c t a n t a n d b e t w e e n t h e$ $t w o p l a n e s . i . e . t h e s p h e r e m u s t$ $l i e i n s i d e a r e g i o n b o u n d e d b y 5$ $p l a n e s .$
Commented by mr W last updated on 19/Aug/24

$t h e q u e s t i o n i s e q u i v a l e n t t o f o l l o w i n g$ $q u e s t i o n : f i n d t h e r a d i u s o f t h e$ $l a r g e s t s p h e r e w h i c h c a n b e c u t$ $f r o m f o l l o w i n g s o l i d o b j e c t :$
Commented by mr W last updated on 19/Aug/24

Commented by ajfour last updated on 25/Aug/24

Commented by mr W last updated on 27/Aug/24

$p l e a s e c h e c k m y a p p r o a c h i n Q 211058$
	Answered by BHOOPENDRA last updated on 18/Aug/24

	$R = m i n (\frac{p}{2}, \frac{q}{2}, \frac{r}{2})$ $T h i s w o u l d b e t h e t h e r a d i u s t h a t$ $c a n b e p l a c e d b e t w e e n t h e t w o p l a n e s$ $i g o t t h i s M r . W .$ $i w r o t e t h e e q u t i o n o f t h e r e d & b l u e$ $p l a n e s f o r t h e p o s i t i o n i n g o f s p h e r e$ $t h e l a r g e s t s p h e r e t h a t c a n f i t b e t w e e n$ $t h e s e p l a n e s i s e q u i d i s t a n c e f r o m$ $b o t h p l a n e s . T h e r a d i u s R o f t h i s$ $s p h e r e w i l l b e e q u a l t o s h o r t e s t d i s t n c e$ $b e t w e e n t w o p l a n e s d i v i d e d b y 2 .$ $I f t h i s i s c o r r e c t A n s t h e n i c a n$ $d o f u r t h e r c a l c u l a t i o n s .$
	Commented by mr W last updated on 19/Aug/24

	$i {d o n}^{'} t h a v e t h e s o l u t i o n . i f y o u$ $t h i n k y o u h a v e a s o l u t i o n, j u s t$ $p o s t i t . t h a n k s!$
	Commented by BHOOPENDRA last updated on 19/Aug/24

	Answered by BHOOPENDRA last updated on 19/Aug/24

	$R e d p l a n e$ $\frac{x}{p} + \frac{y}{q} + \frac{z}{r} = 1$ $N o r m a l v e c t o r {\vec{n}}_{1} = (\frac{1}{p}, \frac{1}{q}, \frac{1}{r}) O r$ $(A_{1}, B_{1}, C_{1}, D_{1})$ $f o r t h e b l u e p l a n e$ $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$ $N o r m a l v e c t o r {\vec{n}}_{2} = (\frac{1}{a}, \frac{1}{b}, \frac{1}{c}) O r$ $(A_{2}, B_{2}, C_{2}, D_{2})$ $t h e d i s t n a c e b e t w e e n t w o p l a n e s$ $A x + B y + C z = D_{1} & A x + B y + C z = D_{2}$ $d = \frac{∣ D_{1} - D_{2} ∣}{\sqrt{A^{2} + B^{2} + C^{2}}}$ $R = m i n m u m d i s t n a c e b e t w e e n p l a n e s \frac{1}{2}$ $I f t h e p l a n e s a r e f a r f r o m e a c h o t h e r$ $S e c o n d$ $R = m i n (\frac{p}{2}, \frac{q}{2}, \frac{r}{2}) o r (\frac{a}{2}, \frac{b}{2}, \frac{c}{2})$ $A s s u m i n g t h e s p h e r e i s c e n t e r e d$ $a t m i d p o i n t b e t w e e n t h e p l a n e s . A n d$ $p l a n e s a r e p a r e l l e l t o e a c h o t h e r .$
	Commented by mr W last updated on 19/Aug/24

	$o n l y w h e n t w o p l a n e s a r e p a r a l l e l,$ $w e c a n s p e a k o f t h e ‘ ‘ {d i s t a n c e}^{″}$ $b e t w e e n t w o p l a n e s . i n g e n e r a l$ $c a s e, t h e t w o p l a n e s a r e n o t p a r a l l e l$ $t o e a c h o t h e r, a n d w e c a n p l a c e a$ $i n f i n i t e l y l a r g e s p h e r e b e t w e e n$ $t h e m . b u t s i n c e t h e s p h e r e m u s t$ $l i e i n t h e f i r s t o c t a n t, t h e s i z e o f$ $t h e s p h e r e i s l i m i t e d .$ $b e s i d e s w e c a n s e e, w h e n p, q, r a r e$ $v e r y s m a l l, t h e r a d i u s o f t h e s p h e r e$ $i s o n l y d e p e n d e n t f r o m a, b, c .$ $y o u r s o l u t i o n s e e m s n o t t o b e$ $c o r r e c t .$
	Commented by BHOOPENDRA last updated on 19/Aug/24

	$Y o u a r e r i g h t M r . W i c o n s i d e r e d$ $p l a n e s a r e p a r a l l e l .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum