حل جملة معادلات

[فخر الدين علولو]

اريد ايجاد نقطة تقاطع ثلاث كرات معروفة المركز و نصف القطر
اريد طريقة الحل !

[The New Mr]

we know that the general equation of sphere is

(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2

for three spheres we have

(x - a*)^2 + (y - b*)^2 + (z - c*)^2 = r*^2.......................... for the first sphere with center (a*, b*, c*) and radius r*

x^2 - 2a*x + a*^2 + y^2 - 2b*y + b*^2 + z^2 - 2c*z + c*^2 = r*^2 .............................. (1)

(x - a**)^2 + (y - b**)^2 + (z - c**)^2 = r**^2 ................. for the second sphere with center (a**, b**, c**) and radius r**

x^2 - 2a**x + a**^2 + y^2 - 2b**y + b**^2 + z^2 - 2c**z + c**^2 = r**^2 .............................. (2)

(x - a***)^2 + (y - b***)^2 + (z - c***)^2 = r***^2 ................. for the second sphere with center (a***, b***, c***) and radius r***

x^2 - 2a***x + a***^2 + y^2 - 2b***y + b***^2 + z^2 - 2c***z + c***^2 = r***^2 .............................. (3)

(2) - (1) will give us that (2a* - 2a**) x + (2b* - 2b**) y + (2c* - 2c**) z = r*^2 - r*^2 .............................. (4)

(3) - (1) will give us that (2a* - 2a***) x + (2b* - 2b***) y + (2c* - 2c***) z = r*^2 - r**^2 ........................ (5)

(3) - (2) will give us that (2a** - 2a***) x + (2b** - 2b***) y + (2c** - 2c***) z = r**^2 - r**^2 .................. (6)

equations (4), (5) and (6) three equations in variables from the first degree we solve them using kramer or guass - jordan

methods we will get the point of intersection

إن كان من توفيق فمن الله وحده وإن كان من خطأ فمنى ومن الشيطان

[فخر الدين علولو]

we know that the general equation of sphere is

(x - a)^2 + (y - b)^2 + (z - c)^2 = r^2

for three spheres we have

(x - a*)^2 + (y - b*)^2 + (z - c*)^2 = r*^2.......................... for the first sphere with center (a*, b*, c*) and radius r*

x^2 - 2a*x + a*^2 + y^2 - 2b*y + b*^2 + z^2 - 2c*z + c*^2 = r*^2 .............................. (1)

(x - a**)^2 + (y - b**)^2 + (z - c**)^2 = r**^2 ................. for the second sphere with center (a**, b**, c**) and radius r**

x^2 - 2a**x + a**^2 + y^2 - 2b**y + b**^2 + z^2 - 2c**z + c**^2 = r**^2 .............................. (2)

(x - a***)^2 + (y - b***)^2 + (z - c***)^2 = r***^2 ................. for the second sphere with center (a***, b***, c***) and radius r***

x^2 - 2a***x + a***^2 + y^2 - 2b***y + b***^2 + z^2 - 2c***z + c***^2 = r***^2 .............................. (3)

(2) - (1) will give us that (2a* - 2a**) x + (2b* - 2b**) y + (2c* - 2c**) z = r*^2 - r*^2 .............................. (4)

(3) - (1) will give us that (2a* - 2a***) x + (2b* - 2b***) y + (2c* - 2c***) z = r*^2 - r**^2 ........................ (5)

(3) - (2) will give us that (2a** - 2a***) x + (2b** - 2b***) y + (2c** - 2c***) z = r**^2 - r**^2 .................. (6)

equations (4), (5) and (6) three equations in variables from the first degree we solve them using kramer or guass - jordan

methods we will get the point of intersection

إن كان من توفيق فمن الله وحده وإن كان من خطأ فمنى ومن الشيطان


شكرا أخي على التفاعل لكن ارجو أن تكمل حل حملة المعادلات لاني قد و صلت الى ما يشبه x=x او 1=1 و ذلك بعد حذف احد المجاهيل مع الشكر و جعله الله في ميزان حسناتك