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If from a point P(a ,b ,c) perpendicular...

If from a point `P(a ,b ,c)` perpendiculars `P A and P B` are drawn to `Y Z and Z X`-planes find the vectors equation of the plane `O A Bdot`

A

`bcx+cay+abz=0`

B

`bcx+acy-abz=0`

C

`bcx-cay+abz=0`

D

`-bcx+cay+abz=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Since, PA, PB are perpendiculars drawn from P(a,b,c) on yz and zx-planes.
`:.` A(0,b,c) and B(a,0,c) are the points on yz and zx=planes
The equation of plane passing through (0,0,0) is
`Ax+By+Cz=0`
which also passes through points A and B.
`:.A*0+B*b+C*c=0`
`andA*a+B*0+C*c=0`
`rArr" "(A)/(bc-0)=(B)/(ac-0)=(C)/(0-ab)=lamda" "` [say]
`rArr" "A=lamdabc,B=lamdaac,C=-lamdaab`
`:.` Required equation is
`bcx+acy-abz=0`
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