(i) It is given that
So we get
= (4 x -2) + (1 x 3) + (-1 x -5)
= -8 + 3 + 5
= 0
Hence, it is proved that the vector(a + b) is perpendicular to vector (a - b)
(ii) It is given that
= 24 - 8 - 16
= 0
Here the dot product of vector(a + b) and vector(a - b) is zero.
Hence, it is proved that the vector(a + b) is orthogonal to vector (a - b)