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

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asked Oct 27, 2024 187k views

1 Answer

Jan Paepke · Answer 1 · 2024-11-03T06:29:26+0000

The direction cosines in different coordinate systems

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