Let a and b be two unit vectors such that |( a + b )+2( a × b )|=2. If θ ∈(0, π) is the angle between a and b, then among the statements: (S1): 2| a…

Let $\displaystyle \hat{a}$ and $\displaystyle \hat{b}$ be two unit vectors such that $\displaystyle |(\hat{a}+\hat{b})+2(\hat{a} \times \hat{b})|=2$. If $\displaystyle \theta \in(0, \pi)$ is the angle between $\displaystyle \hat{\mathrm{a}}$ and $\displaystyle \hat{\mathrm{b}}$, then among the statements: (S1) : $\displaystyle 2|\hat{\mathrm{a}} \times \hat{\mathrm{b}}|=|\hat{\mathrm{a}}-\hat{\mathrm{b}}|$ (S2) : The projection of $\displaystyle \hat{a}$ on $\displaystyle (\hat{a}+\hat{b})$ is $\displaystyle \frac{1}{2}$