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A plane given by 2ax - 3ay + 4az + 6 = 0 passes through the midpoint of the segment joining the centres of the spheres x² + y² + z² + 6x - 8y - 2z = 13 and x² + y² + z² - 10x + 4y - 2z = 8. The value of a is

1. -1
2. 1
3. -2
4. 2

Correct answer: -2

Solution

Centres are (-3,4,1) and (5,-2,1); midpoint (1,1,1). Substituting in 2ax-3ay+4az+6=0: (2-3+4)a + 6 = 0 => 3a = -6 => a = -2.

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