What is the maximum number of rectangular components into which a vector can be split in space?

Explanation

(i) `vec(v)=v_(0) hat(i)+a_(0)b_(0)e^(b_(0)t)hat(k)` (ii) `|vec(v)|=sqrt(v_(0)^(2)+a_(0)^(2)b_(0)^(2)e^(2b_(0)t))` (iii) `vec(a)=a_(0)b_(0)^(2)e^(b_(0)t)hat(k)`