JEE Advanced 2016 Paper 1 Mathematics Q6

Mathematics

Problem

Consider a pyramid

OPQRS

located in the first octant

(x\ge0,\,y\ge0,\,z\ge0)

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