Find the ratio in which the sphere x^{2} + y^{2} + z^{2} = 504 divides the line joining the points (12, -4, 8) and (27, -9, 18). PLZZZZZZ GIVE THE ANSWER BY TODAY ITSELF!!!!!!!!!!!!!!!!. I will give thumbs up to those who will give me the answer!!!!!!!!!!!!!!!!.

Let the sphere meet the line joining the given points at the point (*x*_{1}, *y*_{1}, *z*_{1}).

Then,

Suppose the point (*x*_{1}, *y*_{1}, *z*_{1}) divides the join of the points (12, – 4, 8) and (27, – 9, 18) in the ratio λ : 1.

Then,

Putting these values in equation (1),

Thus, the sphere divides the line joining the given points in the ratio 2 : 3 and 2 : – 3.

Hence, the given sphere divides the line joining the points (12, – 4, 8) and (27, – 9, 18) internally in the ratio 2 : 3 and externally in the ratio 2 : 3.

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