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Question

The volume of the tetrahedron formed by the points (1,1,1),(2,1,3),(3,2,2) and (3,3,4) in cubic units is

A
56
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B
65
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C
5
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D
23
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Solution

The correct option is D 56
Solution:
Let A(1,1,1),B(2,1,3),C(3,2,2) and D(3,3,4)
AB=(21)^i+(11)^j+(31)^k=^i+2^k
AC=(31)^i+(21)^j+(21)^k=2^i+^j+^k
AD=(31)^i+(31)^j+(41)^k=2^i+2^j+3^k
Volume of tetrahedron=16∣ ∣102211223∣ ∣ cubic units
=16[1(32)+0(62)+2(42)] cubic units
=16(1+0+4) cubic units
=56 cubic units
Hence, A is the correct option.

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