If `a=hati+hatj+hatk,b=hati+hatj-hatk`, then vectors perpendicular to a and b is/are

Three vectors a=hati+hatj-hatk, b=-hati+2hatj+hatk and c=-hati+2hatj-hatk , then the unit vector perpendicular to both a+b and b+c is

If two vectors are given as veca = hati - hatj + 2hatk and vecb = hati + 2hatj+hatk , the unit vector perpendicular to both vec a and vec b is

If two vectors are given as veca = hati - hatj + 2hatk and vecb = hati + 2hatj+hatk , the unit vector perpendicular to both vec a and vec b is

A unit vector coplanar with hati + hatj + 2 hatk and hati + 2 hatj + hatk, and perpendicular to hati + hatj + hatk is : a) ((hatj - hatk )/( sqrt2)) b) ((hati + hatj+ hatk )/( sqrt3)) c) ((hati + hatj + 2 hatk )/( sqrt6)) d) ((hati + 2 hatj + hatk )/( sqrt6))

If the position vectors of the three points A,B,C are 2hati+4hatj-hatk, hati+2hatj-3hatk and 3hati+hatj+2hatk respectively, find a vector perpendicular to the plane ABC.