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If OABC is a tetrahedron such that OA^(2...

If OABC is a tetrahedron such that `OA^(2)+BC^(2)=OB^(2)+CA^(2)=OC^(2)+AB^(2)` then

A

`OA bot BC`

B

`OB bot AC`

C

`OC bot AB`

D

`AB bot AC`

Text Solution

Verified by Experts

Let `vec(OA)=veca,vec(OB)=vecb,vec(OC)=vecc`
Then from the given conditions.
`veca.veca+(vecb-vecc).(vecb-vecc)=vecb.vecb+(vecc-veca).(vecc-veca)`
`rArr -2vecb.vecc=-2vecc.veca`
`rArr vecc.(vecb-veca)=0`
`rArr ar(trianglePQR)=1/2xx 4 xx 4=8`
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