Let a and b be two unit vectors such that |(a + b) + 2(a x b)| = 2. If θ ∈ (0, π) is the angle between a and b, then the statements

Question

Let \(\vec a\) and \(\vec b\) be two unit vectors such that \(|(\vec a+\vec b)+2(\vec a\times \vec b)|=2\) If θ ∈ (0, π) is the angle between \(\vec a\) and \(\vec b\), then the statements:

(A) Only (S₁) is true 

(B) Only (S₂) is true 

(C) Both (S₁) and (S₂) are true 

(D) Both (S₁) and (S₂) are false

Answer 1

Correct option is (C) Both (S₁) and (S₂) are true

Now,