# If A, B, C, D Are (1, 1, 1), (2, I, 3), (3, 2, 2), (3, 3, 4) Respectively, Then Find the Volume of Parallelopiped with AB, AC and AD as the Concurrent Edges. - Mathematics and Statistics

If A, B, C, D are (1, 1, 1), (2, I, 3), (3, 2, 2), (3, 3, 4) respectively, then find the volume of parallelopiped with AB, AC and AD as the concurrent edges.

#### Solution

Given that A,B,C and D are (1, 1, 1), (2, 1, 3) , (3, 2, 2) and (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 coterminus edges are a, b and c is [veca vecbvecc]=veca.(vecbxxvecc)

Given that A,B,C and D are (1, 1, 1) , (2, 1, 3) , (3, 2, 2) and (3, 3, 4)

vec(AB)=(2-1)hati+(1-1)hatj+(3-1)hat k

=hati+2hatk

vec(AC)=(3-1)hati+(2-1)hatj+(2-1)hat k

=2hati+hatj+hatk

vec(AD)=(3-1)hati+(3-1)hatj+(4-1)hat k

=2hati+2hatj+3hatk

[veca vecbvecc]=|[1,0,2],[2,1,1],[2,2,3]|

=1(3-2)-0+2(4-2)

=1+4

= 5 cubic units

Concept: Scalar Triple Product of Vectors
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