a - i + j + k , b = j - k , then vector r satisfying a r = b and a r =3 is

Step-by-step solution

Given a r =3 a r = b Let r =x i +y j +z k aligned a r & = | array ccc i & j & k 1 & 1 & 1 x & y & z array | & =( z -y) i - j (z-x)+ k (y-x) aligned Given a r = b (z-y) i -( z -x) j +(y-x) k = j - k Comparing aligned & z -y=0 ... (i) & z -x=-1 ... (ii) & y-x=-1 ... (iii) aligned Also, a r =3 aligned & ( i + j + k )(x i +y j +z k )=3 & x+y+z=3 aligned Solving equations (i), (ii), (iii) and (iv), we get aligned & x= 5 3 , y= 2 3 , z = 2 3 r & = 5 3 i + 2 3 j + 2 3 k aligned