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
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a
the acute angle between OQ and OS is π3
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 32
d
the perpendicular distance from O to the straight line containing RS is 152
answer is B.
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Detailed Solution
Vertices of the pyramid are P(3,0,0),Q(3,3,0),R(0,3,0), T32,32,0,S32,32,3 Angle between OQ&OS is θ⇒cosθ=13 Plane containing OQS is x-y=0 & to RS is x1=y-3-1=z2Perpendicular distance from O to the straight line RS =152