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Question

The volume of a right triangular prism ABCA1B1C1 is equal to 3. If the position vectors of the vertices of the base ABC are A(1,0,1),B(2,0,0) and C(0,1,0), then position vectors of the vertex A1 can be

A
(2,2,2)
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B
(0,2,0)
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C
(0,2,2)
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D
(0,2,0)
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Solution

The correct options are
A (2,2,2)
D (0,2,0)
Multiple answers are available.

A(1,0,1),B(2,0,0),C(0,1,0)

n=AB×AC

=(^i^k)×(^i+^j^k)

n=∣ ∣ijk101111∣ ∣=^i+2^j+^k

A(x,y,z),A(1,0,1)

|AA|=λ|n|

=λ1+4+1=6λ

|n|=6λ

Volume=Area(height)

3=12|n|×h

3=126×h

h=6

|AA|=±|n|=±(^i+2^j+^k)

A=(^i+^k)±(^i+2^j+^k)

A(2,2,2),A(0,2,0)

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