If x, y and z are non-zero real numbers and a =x i +2 j , b =y j +3 k and c =x i +y j +z j are such that a b =z i -3 j + k , then [ a b c ] equals to

Step-by-step solution

Given, a =x i +2 j , b =y j +3 k and c =x i +y j +z k aligned & Now, a b = | array ccc i & j & k x & 2 & 0 0 & y & 3 array | &= i (6-0)- j (3 x-0)+ k (x y-0) &=6 i -3 x j +x y k & 6 i -3 x j +x y k =3 i -3 j + k aligned On equating the coefficients of i , j and k , we get aligned & z=3, x=1 and x y=1 & x y=1 y=1 & a= i +2 j , b = j +3 k & and c = i + j +6 aligned