Consider a pyramid \( O P Q R S \) located in the first octant \( (x \geq 0, y \geq 0, z \geq 0)... VIDEO
Consider a pyramid \( O P Q R S \) located in the first octant \( (x \geq 0, y \geq 0, z \geq 0) \) with \( O \) as origin, and \( O P \) and \( O R \) along the \( X \)-axis and the \( Y \)-axis, respectively. The base \( O P Q R \) of the pyramid is a square with \( O P=3 \). The point \( \mathrm{S} \) is directly above the mid-point \( T \) of diagonal \( O Q \) such that \( T S=3 \). Prove that,
(a) the acute angle between \( O Q \) and \( O S \) is \( \frac{\pi}{3} \)
(b) the perpendicular distance from \( O \) to the straight line containing \( R S \) is \( \sqrt{\frac{15}{2}} \)
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