A vector d→ is equally inclined to three vectors a→=i^−j^+k^,b→=2i^+j^ and c→=3j^−2k^. Let x→,y→,z→  be three vectors in the plane of  a→,b→;b→,c→;c→,a→ respectively. Then

a→=i^−j^+k^,b→=2i^+j^and  c→=3j^−2k^since [a→b→c→]=1−1121003−2=0Therefore,  a→,b→ and c→  are coplanar vectors. Further since d→ is equally inclined to a→,b→ and c→we have ∴    d→⋅a→=d→⋅b→=d→⋅c→=0∴    d→⋅x→=d→⋅y→=d→⋅z→=0∴    d→⋅r→=0