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Given any 2 points $p_1, p_2 \neq p_1$ on a sphere, how can we check if $p_3$ is on the geodesic from $p_1$ to $p_2$?

I think of checking the $||\text{arc } p_1 p_3|| + ||\text{arc } p_3 p_2|| = ||\text{arc } p_1 p_2||$. Is this condition sufficient? Any other suggestions?

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  1. Evaluate the following double integral $$ \int_{0}^{\frac{\pi}{2}} \int_{0}^{\pi}\left(x^{2} \cos y-\sin x\right) d x d y $$
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    $\begingroup$ Would you mind show me why this makes sense? $\endgroup$
    – Yuki.F
    Feb 14, 2021 at 4:21

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