If $\vec a$ and $\vec b$ are two unit vectors such that $\vec a + \vec b$ is also a unit vector, then find the angle between $\vec a$ and $\vec b$ is
Answer & explanation
Correct answer: option 4
Since $\vec a$ and $\vec b$ are unit vectors, $(\vec a+\vec b) . (\vec a+\vec b) = 1$
$⇒ \vec a.\vec a+\vec b.\vec b+2\vec a.\vec b=1$
$⇒1+1+ 2\vec a.\vec b=1⇒\vec a.\vec b= -1/2$
Hence the angle θ between $\vec a$ and $\vec b$ is given by
$cosθ = -1/2⇒ θ =120°$
Hence (D) is the correct answer.