Hello this is not a homework, just studying for the exam, and : 1. The problem statement, all variables and given/known data Consider E a linear space with dot product (.,.) and the norm ||x|| = sqrt(x,x) a and b two orthogonals elements of E Find the value of ||a+ b|| et||a- b|| and ||a+ b||-||a- b|| 2. Relevant equations 3. The attempt at a solution a and b orthogonals means that ||a||=||b||=1 ||a+b||=√(a+b,a+b) = √[(a,a)+(b,a)+(a,b)+(b,b) ] =√[ 1+0+0+1 ] = √2 ||a-b||=√(a-b,a-b) = √[(a,a)+(-b,a)+(a,-b)+(-b,-b) ] =√[ 1-(b,a)+(-b,a)*-1 ] = √[ 1-(b,a)-(b,a)*-1 ]=0 ||a+b||-||a-b||=√2 Is that correct ?