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 ORalongthe x-axis and the y-axis, respectively. The base OPQR of the pyramid is a square with OP =3. Thepoint 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 $$\sqrt{\frac{15}{2}}$$