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