Express the vector as sum of two vectors such that one is parallel to the vector and the other is perpendicular to .

Solution:

Let be written as sum of , where is parallel to and is perpendicular to
Let

So according to the question
for some constant


Also is perpendicular to


Comparing left hand side and right hand side in I




Hence now we can calculate d1, d2, d3 from equations III, IV and V as