Let $a$ and $b$ be two unit vectors such that $| ( a + b ) + 2 ( a \times b ) | = 2$. If $\theta \in ( 0 , \pi )$ is the angle between $\hat { \mathrm { a } }$ and $\widehat { \mathrm { b } }$, then among the statements: $( S 1 ) : 2 | \widehat { a } \times \hat { b } | = | \widehat { a } - \hat { b } |$ $( S 2 )$ : The projection of $\widehat { a }$ on $( \widehat { a } + \widehat { b } )$ is $\frac { 1 } { 2 }$ (1) Only $( S 1 )$ is true. (2) Only $( S 2 )$ is true. (3) Both $( S 1 )$ and $( S 2 )$ are true. (4) Both $( S 1 )$ and $( S 2 )$ are false.
Let $a$ and $b$ be two unit vectors such that $| ( a + b ) + 2 ( a \times b ) | = 2$. If $\theta \in ( 0 , \pi )$ is the angle between $\hat { \mathrm { a } }$ and $\widehat { \mathrm { b } }$, then among the statements:\\
$( S 1 ) : 2 | \widehat { a } \times \hat { b } | = | \widehat { a } - \hat { b } |$\\
$( S 2 )$ : The projection of $\widehat { a }$ on $( \widehat { a } + \widehat { b } )$ is $\frac { 1 } { 2 }$\\
(1) Only $( S 1 )$ is true.\\
(2) Only $( S 2 )$ is true.\\
(3) Both $( S 1 )$ and $( S 2 )$ are true.\\
(4) Both $( S 1 )$ and $( S 2 )$ are false.