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Let a and b be two unit vectors. If the vectors c = a + 2b and d = 5a - 4b are perpendicular to each other, then the angle between a and b is:

1. π/6
2. π/2
3. π/3
4. π/4

Correct answer: π/3

Solution

The vectors c and d being perpendicular means their dot product is zero. By substituting the expressions for c and d and using the properties of unit vectors, we can derive the cosine of the angle between a and b, leading to the conclusion that the angle is π/3.

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