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If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors, the angle between these vectors is:

1. 180°
2. 0°
3. 90°
4. 45°

Correct answer: 90°

Solution

If \(|\vec a+\vec b| = |\vec a-\vec b|\), then squaring both sides gives \(a^2+b^2+2ab\cos\theta = a^2+b^2-2ab\cos\theta\). This implies \(\cos\theta = 0\), so the angle is 90°.

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