(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I was trying to figure out how to derive acceleration in spherical coordinates, and I realized that I need to find the projection of each spherical unit vector [ e(r), e(θ), and e(φ)] onto each Cartesian unit vector [î, j, and k], but I'm not quite sure as to how to do that. It's pretty intuitive for me to calculate the projections of e(r), but the other components confuse me a bit.

2. Relevant equations

see attached image

3. The attempt at a solution

I've attached the work I've done so far as an image (I didn't mean for that ' near the î on the bottom to be there..)

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# Trying to derive equation for acceleration in spherical coordinate system

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