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If the angle between two unit vectors a-hat and b-hat is 60 degrees, find |a-hat - b-hat|.

1. 0
2. 1
3. 2
4. 4

Correct answer: 1

Solution

For unit vectors a-hat and b-hat with angle 60 deg between them: |a-hat - b-hat|² = |a-hat|² + |b-hat|² - 2*(a-hat. b-hat) = 1 + 1 - 2*cos(60 deg) = 2 - 2*(1/2) = 2 - 1 = 1. So |a-hat - b-hat| = sqrt(1) = 1.

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