If ( a = i + j +2 k ; b = i + j - k ) are orthogonal and ( | a |=| b | ) then ( ( , )= )

Step-by-step solution

Given vectors, [ array l a = i + j +2 k (1) b = i + j - k (2) array ] For vectors to be orthogonal, we have [ array l a b =0 ( i + j +2 k ) ( i + j - k )=0 + -2=0 + =2 (3) and | a |=| b | 1+ ²+4 = ²+1+1 1+ ²+4= ²+1+1 (4) array ] From Eqs. (3) and (4), we get [ array l ²+3= ²=(2 )² ²+3=4+ ²-4 So, = 1 4 =2- 1 4 = 7 4 array ] [ Hence ( , )= ( 1 4 , 7 4 ) ]