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If OABC is a tetrahedron such thatOA^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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