i. If and show that is perpendicular to

ii. If and then show that and are orthogonal.

i)

Now

= (4 × - 2) + (1 × 3) + ( - 1 × - 5) = - 8 + 3 + 5 = 0

Since the dot product of these two vectors is 0,the vector is perpendicular to

Hence,proved.

ii)

Now

= (6 × 4) + (2 × - 4) + ( - 8 × 2) = 24 - 8 - 16 = 0

Since the dot product of these two vectors is 0,the vector is perpendicular to

Hence,proved that and are orthogonal.