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If the magnitudes of the vectors a + b and a − b are equal, then the vectors a and b represent

1. a rectangle
2. a square
3. a rhombus
4. none of these

Correct answer: a rectangle

Solution

|a+b|^2=|a-b|^2 gives 4(a.b)=0, so a and b are perpendicular. As adjacent sides of a parallelogram, perpendicular sides form a rectangle (a square would also require equal magnitudes, which is not given).

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