If p = i + j + k and q = i -2 j + k . Then a vector of magnitude 5 3 units perpendicular to the vector q and coplanar with p and q is

Step-by-step solution

Let r =a i +b j +c k As r is perpendicular to q . array ll r q =0 a-2 b+c=0 ...(i) array Also, r is coplanar with vectors p and q aligned & [ array ccc p & q & - r array ]=0 & | array ccc 1 & 1 & 1 1 & -2 & 1 a & b & c array |=0 & 3 a -3 c =0 & a - c =0 & a = c ...(ii) aligned From (i) and (ii), we get b = c - r = i + j + k ^ s Now, the magnitude of required vector is 5 3 units. aligned Required vector & =5 3 r r & =5 3 i + j + k 3 =5( i + j + k ) aligned