10%20-%20Sphere

10%20-%20Sphere - PROBLEMS 10 SPHERE Page 1 1 Find the...

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PROBLEMS 10 - SPHERE Page 1 ( 1 ) Find the equations in vector as well as Cartesian form of a sphere with centre ( 2, 3, 4 ) and passing through ( 4, 4, 4 ). [ Ans: l r l 2 - 2 ( 2, 3, 4 ) r + 24 = 0, x 2 + y 2 + z 2 - 4x - 6y - 8z + 24 = 0 ] ( 2 ) Find the centre and length of radius of the sphere 2 r - r ( 3, 1, - 1 ) + 2 = 0. 2 3 , 2 1 , 2 1 , 2 3 : Ans - ( 3 ) Find the centre and radius of the sphere represented by 2x 2 + 2y 2 + 2z 2 - 4x + 1 = 0. 2 1 ), 0 0, 1, ( : Ans ( 4 ) Obtain the equation, the centre and length of a radius of the sphere through ( 0, 0, 0 ), ( a, 0, 0 ), ( 0, b, 0 ) and ( 0, 0, c ). + + + + = c b a 2 1 0, cz by ax z y x : Ans 2 2 2 2 2 2 - - - ( 5 ) If the diameter of the sphere has end-points ( 1, 2, - 1 ) and ( 2, 1, 0 ), obtain the equation of the sphere. [ Ans: x 2 + y 2 + z 2 - 3x - 3y + z + 4 = 0 ] ( 6 ) Derive the equation of the sphere through ( 0, 0, 0 ), ( - a, b, c ), ( a, - b, c ) and ( a, b, - c ). + + + + + + c
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This note was uploaded on 11/28/2011 for the course MATH 300 taught by Professor Jones during the Spring '06 term at ITT Tech Flint.

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10%20-%20Sphere - PROBLEMS 10 SPHERE Page 1 1 Find the...

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