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-

  1. the acute angle between OQ and OS is π/3
  2. the equaiton of the plane containing the triangle OQS is x – y = 0
  3. the length of the perpendicular from P to the plane containing the triangle OQS is 3/√3
  4. the perpendicular distance from O to the straight line containing RS is √(15/2)
Anurag Mishra Professor Asked on 23rd May 2016 in Maths.
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Answer: (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 3/√2
(d) the perpendicular distance from O to the straight line containing RS is √(15/2)

Anurag Mishra Professor Answered on 24th May 2016.
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