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Q.

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
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