question_answer

Consider a pyramid OPQRS located in the first octant \[(x\ge 0,\,\,y\ge 0,\,\,z\ge 0)\]  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 \[\Delta OQS\] is \[x-y=0.\]

C)  the length of the perpendicular from p to the plane containing the \[\Delta OQS\] is \[\frac{1}{\sqrt{2}}\].

D)  the perpendicular distance from O to the straight line containing RS is \[\sqrt{\frac{13}{2}}\].

E)  None of these