How do I express Z and R unit vectors in different coordinate systems?

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SUMMARY

The discussion focuses on expressing the Z unit vector in spherical coordinates and the R unit vector in rectangular coordinates at the point T(2,3,-4). The spherical coordinates for point T are given as (5.385, -42 degrees, 56.3 degrees). To convert unit vectors between coordinate systems, one must transform the coordinates accordingly, utilizing the known rectangular unit vector (1,0,0) for the X-axis. This transformation is essential for accurately representing vectors in different coordinate systems.

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zekester
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at point T(2,3,-4) in rectangular coordinate system, how would I express the Z unit vector in the spherical system and the R unit vector in the rectangular system? I know T in spherical coordinates is (5.385,-42 degrees,56.3 degrees) but i have no idea how i would express a unit vector in a different coordinate system.
 
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The x unit vector is the vector (1,0,0) in the rectangular coordinate system. So all you need to do is transform the coordinates from one system to the other.
 

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