Determine the direction cosines of a vectorÂ
The vector is given by,
            Â
The X, Y and Z components of the vector are,Â
∴  ,,          Â
So, the resultant of the vector is given by,
    Â
Thus,Â
Direction cosine is,Â
Find Z component of resultant of vectors,
 and .
Resultant ofÂ
    is the Z component of vector.
Therefore Z component of resultant of  is zero.
If  are the magnitudes of rectangular components of velocity vector of magnitude v, then
         Â
Given,
         and   Â
∴        Â
     Â
That is,
        , is the magnitude of other rectangular component of velocity.Â
The vertical component ofvelocity of the airplane will give us the velocity with which the airplane moves away from the Earth.Â
As the aeroplane takes off at angle  with horizontal,Â
 ∴       Â
∴         Â