Question

If from a point `P(a ,b ,c)` prpendiculars `P Aa n dP B` are drawn to `y za n dz x-p l a n e s ,` find the eqution of th plane `O A Bdot`
A. `bcx+cay+abz=0`
B. `bcx+cay-abz=0`
C. `bcx-cay+abz=0`
D. `-bcx+cay+abz=0`

Answer 1

Correct Answer - B
The coordinates of A and B are `(0,b,c)` and `(a,0,c)` respectively.
The equation of a plane passing through `O(0,0,0)` is
`Px+Qy+Rz=0`………….i
It passes through A and B
`:.Pxx0+Qxxb+Rxxc=0`
and `Pxxa+Qxx0+Rxxc=0`
`impliesP/(bc)=Q/(ac)=R/(-ab)`
Subsituting the value of `P,Q` and `R` in (i) we get
`bcx+acy-abz=0`