let where u is vector parallel to b and v is vector perpendicular to b, as given in the question.

So, ; where p is some constant

Substituting this value in above equation

Now according to conditions since vector v and b are perpendicular to each other

(5 – 3p) (3) +(5 – p) =0

15 – 9p + 5 – p = 0

20 = 10p

P = 2

So,

substituting this value in above equation, we will get