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3D Geometry question

2016 · Shift 1 · Q20

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PYQ Library
JEE Advanced
Mathematics
3D Geometry
2016 · Shift 1 · Q20

3D Geometry question

2016 · Shift 1 · Q20

JEE AdvancedMathematics3D GeometryMultiple correct+4 / −2

Consider a pyramid

OPQRS

located in the first octant

\left( {x \ge 0,y \ge 0,z \ge 0} \right)

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 ${\pi \over 3}$
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 ${3 \over {\sqrt 2 }}$
D
the perpendicular distance from $O$ to the straight line containing $RS$ is $\sqrt {{{15} \over 2}}$

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