If a = i +2 j + k , b = i - j + k , c = i + j - k , then a vector in the plane of a and b , whose projection on c is 1 3 , is

Step-by-step solution

Let r be the vector coplanar to a and b . Then, aligned r & = a + m b & =( i +2 j + k )+ m ( i - j + k ) & = i (1+ m )+ j (2- m )+ k (1+ m ) aligned Since the projection of r along c is 1 3 , aligned & r c c = 1 3 & (1+ m )+(2- m )-(1+ m ) 3 = 1 3 & (1+ m )+(2- m )-(1+ m )= 1 & m =3 or m =1 aligned Substituting m =3 in equation (i), we get aligned & r = i (1+3)+ j (2-3)+ k (1+3) & r =4 i - j +4 k aligned