Question

If (2, 3, 5) is one end of a diameter of the sphere x² + y² + z² - 6x − 12y − 2z + 20 = 0, then the coordinates of the other end of the diameter are 

(A) (4, 9, -3) 

(B) (4, -3, 3) 

(C) (4, 3, 5) 

(D) (4, 3, -3)

Answer 1

Answer is (A) (4, 9, -3)

Coordinates of the centre is

(-(-6)/2, -(-12)/2, -(-2)/2) = (3, 6, 1)

Let the coordinates of the other end of the diameter be (a, b, g ). (See Fig.) 

Therefore,

(α + 2)/2 = 3; (β + 3)/2 = 6; (γ + 5)/2 = 1

Hence, α = 4, β = 9 and  γ = - 3.