Consider a pyramid $OPQRS$ located in the first octant $(x \geq 0, y \geq 0, z \geq 0)$ with $O$ as origin, and $OP$ and $OR$ along the $x$-axis and the $y$-axis, respectively. The base $OPQR$ of the pyramid is a square with $OP = 3$. The point $S$ is directly above the mid-point $T$ of diagonal $OQ$ such that $TS = 3$. Then (A) the acute angle between $OQ$ and $OS$ is $\frac{\pi}{3}$ (B) the equation of the plane containing the triangle $OQS$ is $x - y = 0$ (C) the length of the perpendicular from $P$ to the plane containing the triangle $OQS$ is $\frac{3}{\sqrt{2}}$ (D) the perpendicular distance from $O$ to the straight line containing $RS$ is $\sqrt{\frac{15}{2}}$
Consider a pyramid $OPQRS$ located in the first octant $(x \geq 0, y \geq 0, z \geq 0)$ with $O$ as origin, and $OP$ and $OR$ along the $x$-axis and the $y$-axis, respectively. The base $OPQR$ of the pyramid is a square with $OP = 3$. The point $S$ is directly above the mid-point $T$ of diagonal $OQ$ such that $TS = 3$. Then\\
(A) the acute angle between $OQ$ and $OS$ is $\frac{\pi}{3}$\\
(B) the equation of the plane containing the triangle $OQS$ is $x - y = 0$\\
(C) the length of the perpendicular from $P$ to the plane containing the triangle $OQS$ is $\frac{3}{\sqrt{2}}$\\
(D) the perpendicular distance from $O$ to the straight line containing $RS$ is $\sqrt{\frac{15}{2}}$