If a^2 + b^2 + c^2 = x^2 + y^2 + z^2 = 1, then ax + by + cz is

1) > 1

2) < 1

3) > 0

4) < 0

Solution: (2) < 1

Since AM > GM

[a² + x²] / 2 > √a²x²

[a² + x²] > 2ax

[b² + y²] > 2by

[c² + z²] > 2cz

a² + x² + b² + y² + c² + z² > 2 (ax + by + cz)

(a² + b² + c²) + (x² + y² + z²) > 2 (ax + by + cz)

1 + 1 > 2 [ax + by + cz] [ax + by + cz] < 1

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If a² + b² + c² = x² + y² + z² = 1, then ax + by + cz is