If a = i + j + k , c = j - k , a b = c and a b =1 , then b

Step-by-step solution

Let b =x i +y j +z k and we have a b =1 aligned & ( i + j + k )(x i +y j +z k )=1 x+y+z=1 & a b = c | array lll i & j & k 1 & 1 & 1 x & y & z array |= j - k & (z-y) i -(z-x) j +(y-x) k = j - k & z-y=0, x-z=1, y-x=-1 & y=z, z=x-1, y=x-1 & Thus b =x i +(x-1) j +(x-1) k & x+(x-1)+(x-1)=1 & x=1, y=0, z=0 & b = i aligned