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Three vectors a, b, and c satisfy a + b + c = 0. If |a| = 1, |b| = 2, and |c| = 3, then the value of a·b + b·c + c·a is

1. 1
2. 0
3. −7
4. 7

Correct answer: −7

Solution

The equation a + b + c = 0 implies that c = -a - b. By substituting this into the expression a·b + b·c + c·a and using the magnitudes of the vectors, we can derive that the result simplifies to -7, confirming the correct answer.

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