Express as the sum of a vector parallel and a vector perpendicular to
Let and
let where u is vector parallel to b and v is vector perpendicular to b.
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
2(2 – 2p) – 4(1 + 4p) – 2(3 + 2p) = 0
4 – 4p – 4 – 16 p – 6 – 4p = 0
– 24 p = 6
Substituting this value of u vector in above equation