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The volume of a right triangular prism A...

The volume of a right triangular prism `ABCA_1B_1C_1` is equal to 3. If the position vectors of the vertices of thebase ABC are `A(1, 0, 1), B(2,0, 0) and C(O, 1, 0)`, then position vectors of the vertex `A_1`, can be

A

`(-2,0,2)`

B

`(0,-2,0)`

C

`(0,2,0)`

D

`(2,2,2)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
Volume = Area of base `xx` height

`3=1/2 xx sqrt(2) xx sqrt(3) xxh`
`rArr h=sqrt(6)`
`(A_(1)A)^(2)=h^(2)=6`
`vec(A_(1)A).vec(A.B)=0`
`vec(A_(1)A).vec(AC)=0`
`vec(A(A_(1))).vec(BC)=0`
Solving we get position vector of `A_(1)` as (0,-2,0) or (2,2,2).
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