Question

तीन दिए गये बिन्दुओं (1,0,0), (0, 1,0) तथा (0,0, 1) से जाते हुए, गोलों की संख्या है

Answer 1

first question answer is 7 next is 6

Answer 2

Given :  बिन्दु (1,0,0), (0, 1,0) तथा (0,0, 1)  

points (1,0,0), (0, 1,0) and (0,0, 1)  

To Find : तीन दिए गये बिन्दुओं  से जाते हुए, गोलों की संख्या  

Number of spheres pas sing through these three points

Solution:

Equation of sphere

(x-h)² + (y-k)² + (z - l)² = r²

(h , k , l )  center of Sphere

r = radius of Sphere

Let say Sphere center is ( x , y , z) and radius is r

then

(x - 1)² + y² + z²  = r²   Eq1

x² + (y - 1)² + z² = r²   Eq2

x² + y² + (z - 1)² = r²   Eq3

From Eq1 and Eq2

(x - 1)² + y² + z²   = x² + (y - 1)² + z²

=>  -2x  = - 2y

=> x = y

similarly from Eq 1, Eq3  and  Eq2 Eq3

x = z  and y = z

from all

x = y = z

Hence there exist infinite points satisfying  x = y = z

Hence infinite spheres pas sing through points (1,0,0), (0, 1,0) and (0,0, 1)  

तीन दिए गये बिन्दुओं (1,0,0), (0, 1,0) तथा (0,0, 1) से जाते हुए, गोलों की संख्या अनगिनत है

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