Let the vector be given as For this vector to be coplanar with and we will have

This gives, .....(i)

.....(ii)

.....(iii)

For the vector to be perpendicular to we will have

......(iv)

Adding equation (i) to (iii), we get

Now with the help of (i), (ii) and (iii), we get

Hence the required vector is

To be its unit vector

Hence the required unit vector is, .

Trick : Check for option is a unit vector and perpendicular to .

But .

So it is not coplanar with the given vector.

Check for option is a unit vector and also perpendicular to .

So, it is also coplanar with the given vectors.