Duration: 14:13

32 views

0

Consider a pyramid OPQRS located in the first octant \( (\mathrm{x} \geq 0, \mathrm{y} \geq 0, \mathrm{z} \geq 0 \) ) with \( \mathrm{O} \) as origin, and OP and OR along the \( x \)-axis and the \( y \)-axis, respectively. The base OPQR of the pyramid
\( \mathrm{P} \) is a square with \( \mathrm{OP}=3 \). The point \( \mathrm{S} \) is directly above the mid-point \( \mathrm{T} \) of diagonal \( \mathrm{OQ} \) such that \( \mathrm{TS}=3 \). Then-
W
(A) the acute angle between OQ and OS is \( \frac{\pi}{3} \).
(B) the equaiton of the plane containing the triangle OQS is \( x-y=0 \)
(C) the length of the perpendicular from \( \mathrm{P} \) to the plane containing the triangle OQS is \( \frac{3}{\sqrt{2}} \)
(D) the perpendicular distance from \( \mathrm{O} \) to the straight line containing RS is \( \sqrt{\frac{15}{2}} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live