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If C is the midpoint of the line segment AB and P is any point not lying on AB, then which relation is true?

1. PA + PB = 2PC
2. PA + PB = PC
3. PA + PB + 2PC = 0
4. PA + PB + PC = 0

Correct answer: PA + PB = 2PC

Solution

The correct option states that the sum of the vectors from point P to points A and B equals twice the vector from P to the midpoint C. This relationship holds true because the midpoint C divides the segment AB into two equal parts, making the distances PA and PB symmetrical around C.

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