VIAMC 2025 Mock Test — Level 6 (Senior) Question 6

At an airport, an airplane is represented by $M$ in the coordinate space $Oxyz$, as shown. Let $H$ be the orthogonal projection of $M$ onto $(Oxy)$. Given $OM=50$, $\angle(\vec i,\overrightarrow{OH})=64^\circ$ and $\angle(\overrightarrow{OH},\overrightarrow{OM})=48^\circ$, find the coordinates of $M$, rounded to one decimal place.

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