Consider a pyramid OPQRS located in the first octant `(xge0, yge0, zge0)` with O as origin and OP and OR along the X-axis and the Y-axis , respectively. The base OPQRS 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,

Options

A. `x-y=0`
B. `y-z=0`
C. `z-x=0`
D. `x-y-z=0`

Answer

A

Explanation

The equation of a plane pasing through `O(0,0,0)` is
`a(x-0)+b(y-0)+c(z-0)=0`……………i

If it passes through `Q(3,3,0)` and `S(3//2,3//2,3)`, then
`3a+3b+0c=0`
and `3/2a+3/2b+3c=0`
`:.a/9=b/(-9)=c/(9/2-9/2)` or `a/1=b/(-1)=c/0`
Substituting the values of a,b and c in (i) we obtain `x-y-0` as the equation of the required plane.