If A (1,-1,0), B (0,1,-1) and C (-1,0,1) , then the unit vector d such that a and d are perpendiculars and b , c , d are coplanar is

Step-by-step solution

Let d =p i +q j +r k , where p, q, r R As b , c , d are coplanar, we get array ll & | array ccc 0 & 1 & -1 -1 & 0 & 1 p & q & r array |=0 & -1(-r-p)-1(-q)=0 ...(i) & p+q+r=0 array Also, given that a and d are perpendiculars. array ll & a ~d =0 & p - q =0 & p = q ...(ii) array Among the given options only option (C) satisfies equations (i) and (ii)