Question

Find the direction cosines and direction angles of the vector.

A) In spherical coordinates
B) In cylindrical coordinates
C) In rectangular coordinates
D) In polar coordinates

Answer 1

The direction cosines in different coordinate systems

Step-by-step explanation:

In spherical coordinates, the direction cosines of a vector are given by:

cos(theta) = x/r

cos(phi) = z/r

In cylindrical coordinates, the direction cosines of a vector are given by:

cos(phi) = x/r

cos(theta) = y/sqrt(x^2+y^2)

In rectangular coordinates, the direction cosines of a vector are given by:

cos(alpha) = Ax/|A|

cos(beta) = Ay/|A|

cos(gamma) = Az/|A|

In polar coordinates, the direction cosines of a vector are given by:

cos(phi) = x/r

cos(theta) = y/r