Let veca and vecb be two unit vectors, and θ is the angle between them. Then veca + vecb is a unit vector if ______.

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Let veca and vecb be two unit vectors, and $\theta$ is the angle between them. Then veca + vecb is a unit vector if underline(theta = (2pi)/3). Explanation: Let veca and vecb be unit vectors and $\theta$ is the angle between them, Then |veca| = |vecb| = 1 Now veca + vecb is a unit vector if |veca + vecb| = 1 |veca + vecb| = 1 (veca + vecb)^2 = 1 `(veca + vecb) xx (veca + vecb) = 1 veca xx veca + veca xx vecb + vecb xx veca + vecb xx vecb = 1 |a|^2 + 2a xx b + |b|^2 = 1 1^2 + 2|veca||vecb|costheta + 1^2 = 1 1 + 2.1.1costheta + 1 = 1 cos theta = (-1)/2 theta = (2pi)/3 Hence, veca + vecb is a unit vector if theta = (2pi)/3 The correct answer is (2pi)/3`.

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