If a = i + j , b =2 j - k and r a = b a , r b = a b , then the value r | r | is

Step-by-step solution

Let r =x i +y j +z k then aligned & r a = b a ( r - b ) a = 0 & | array ccc i & j & k x & y-2 & z +1 1 & 1 & 0 array |= 0 & (- z -1) i -(- z -1) j +(x-y+2) k = 0 & z =-1, x-y=-2 aligned Now, r b = a b =( r - a ) b = 0 aligned & | array ccc i & j & k x-1 & y-1 & z 0 & 2 & -1 array |= 0 & (1-y-2 z ) i -(1-x) j +(2 x-2) k = 0 & 1-y-2 z=0, x=1 aligned Solving (i) and (ii), we get aligned & x=1, y=3, z=-1 & r = i +3 j - k & | r |= 1+9+1 = 11 & r |- r - | = i +3 j - k 11 aligned