# Consider a pyramid OPQRS located in the first octant (x > 0,y > 0, z > 0) with O

Consider a pyramid OPQRS located in the first octant (x __> __0,y __> __0, z __> __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-

- the acute angle between OQ and OS is π/3
- the equaiton of the plane containing the triangle OQS is x – y = 0
- the length of the perpendicular from P to the plane containing the triangle OQS is 3/√3
- the perpendicular distance from O to the straight line containing RS is √(15/2)

**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 3/√2**

(d) **the perpendicular distance from O to the straight line containing RS is √(15/2)**