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If the volume of tetrahedron A B C D ...

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=0`

B

`y+x=6`

C

`y+z=0`

D

`y+z=-3`

Text Solution

Verified by Experts

The correct Answer is:
b, c
Volume of tetrehedron `ABCD= (1)/(6) |[vec(AB)vec(AC)vec(AD)]|= 1` cubic units.
`rArr" " |{:(-1,,1,,-1),(1,,1,,-1),(x-0,,y-1,,z-2):}|= pm 6`
or `" "-2(y-1)-2(z-2)= pm 6`
or `" "y-1+z-2= pm 3`
`rArr" "y+z=6 or y+z=0`
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