A unit vectors coplanar with i + j +2 k and i +2 j + k and perpendicular to i + j + k is

Step-by-step solution

aligned Let a & =t( i + j +2 k )+s( i +2 j + k ) & =(t+3 s) i +(t+2 s) j +(2 t+s) k aligned given, a ( i + j + k )=0 t+s+t+2 s+2 t+s=0 array rrr & 4(t+s)=0 & t+s=0 array a =t( 1 + j +2 k )-t( i +2 j + k )=t(-1+ k ) aligned & But | a |=1 & 1=2 t^2 aligned t= 1 2 a= ( k-j 2 )