Consider a pyramid located in the first octant ( ) with as origin and and along the…

MATHEMATICS · Multi-part · A Level · Mathematics · Vectors · Vectors

Problem

Consider a pyramid

OPQRS

located in the first octant (

x \ge 0, y \ge 0, z \ge 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, [More than One Correct Type Question, 2016 Adv.] (a) the acute angle between

OQ

and

OS

\frac{\pi}{3}

(b) the equation of the plane containing the

\triangle OQS

x - y = 0

P

to the plane containing the

\triangle OQS

\frac{3}{\sqrt{2}}

(d) the perpendicular distance from

O

to the straight line containing

RS

\sqrt{\frac{15}{2}}