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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`

Text Solution

Verified by Experts

The correct Answer is:
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`
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