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If the volume of tetrahedron `A B C D` is 1 cubic units, where `A(0,1,2),B(-1,2,1)a n dC(1,2,1),` then the locus of point `D` is a. `x+y-z=3` b. `y+z=6` c. `y+z=0` d. `y+z=-3`

A

x+y-z=3

B

y+z=6

C

y+z=-3

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
2
`A(0,1,2),B(-1,2,1),C(1,2,1)& D(u,v,w)`
(volume of tetralfhedrom ABCD)
`|(1)/(6)[overset(rarr)(AB" ")overset(rarr)(AC" ")overset(rarr)(AD" ")]=1` cubic units
`=|{:(-1,1,-1),(" "1,1,-1),(u-0,v-1,w-2):}|`
`rArr{:{(y-1+z-2=+-3),(y+z=6 or y+z=0):}`
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