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Question
If A,B,C,D are (1,1,1),(2,1,3),(3,2,2),(3,3,4) respectively, then find the volume of the parallelopiped with AB,AC and AD as the concurrent edges.
If A,B,C,D are (1,1,1),(2,1,3),(3,2,2),(3,3,4) respectively, then find the volume of the parallelopiped with AB,AC and AD as the concurrent edges.
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Solution
The correct option is B 5 cubic units
Given that A,B,C,D are (1,1,1),(2,1,3),(3,2,2),(3,3,4) respectively. We need to find the volume of the parallelopiped with AB,AC and AD as the concurrent edges.
The volume of the parallelopiped whose edges are →a,→b,→c is [→a→b→c]=→a.(→b×→c)
−−→AB=(2−1)^i+(1−1)^j+(3−1)^k=^i+2^k
−−→AC=(3−1)^i+(2−1)^j+(2−1)^k=2^i+^j+^k
−−→AD=(3−1)^i+(3−1)^j+(4−1)^k=2^i+2^j+3^k
[−−→AB−−→AC−−→AD]=∣∣
∣∣102211223∣∣
∣∣
=1(3−2)−0+2(4−2)
=1+4
=5 cubic units
Given that A,B,C,D are (1,1,1),(2,1,3),(3,2,2),(3,3,4) respectively.
We need to find the volume of the parallelopiped with AB,AC and AD as the concurrent edges.
The volume of the parallelopiped whose edges are →a,→b,→c is [→a→b→c]=→a.(→b×→c)
−−→AB=(2−1)^i+(1−1)^j+(3−1)^k=^i+2^k
−−→AC=(3−1)^i+(2−1)^j+(2−1)^k=2^i+^j+^k
−−→AD=(3−1)^i+(3−1)^j+(4−1)^k=2^i+2^j+3^k
[−−→AB−−→AC−−→AD]=∣∣ ∣∣102211223∣∣ ∣∣
=1(3−2)−0+2(4−2)
=1+4
=5 cubic units
The volume of the parallelopiped whose edges are →a,→b,→c is [→a→b→c]=→a.(→b×→c)
−−→AB=(2−1)^i+(1−1)^j+(3−1)^k=^i+2^k
−−→AC=(3−1)^i+(2−1)^j+(2−1)^k=2^i+^j+^k
−−→AD=(3−1)^i+(3−1)^j+(4−1)^k=2^i+2^j+3^k
[−−→AB−−→AC−−→AD]=∣∣ ∣∣102211223∣∣ ∣∣
=1(3−2)−0+2(4−2)
=1+4
=5 cubic units
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