If a → = ( 1 , 1 , 0 ) , b → = ( 1 , 1 , 1 ) , then unit vector in the plane of a → and b…

Let, $\overrightarrow{u} = x\hat{i}+y\hat{j}+z\hat{k}$ is the required vector

$\left|\overrightarrow{u}\right| = \sqrt{x^2+y^2+z^2}=1$, since it is a unit vector

Vectors in option $1$ and $3$ are the only units vectors

Also, $\overrightarrow{a}$ is perpendicular to the vector so there dot product must be zero

Only $\overrightarrow{a}.\hat{k} = 0$

Hence, options $3$ is the correct answer.