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  • Volume of tetrahedron ABCD, where A has co-ordinates (1,0,0), B has co-ordinates (1,2,0), C has co-ordinates (2,2,2) and D has co-ordinates (0,3,2) isOption

Volume of tetrahedron ABCD, where A has co-ordinates (1,0,0), B has co-ordinates (1,2,0), C has co-ordinates (2,2,2) and D has co-ordinates (0,3,2) is

Option: 1

\frac{4}{3} cubic units


Option: 2

\frac{2}{3} cubic units


Option: 3

8 cubic units


Option: 4

\frac{1}{3} cubic units


Answers (1)

best_answer

Fig 10

 

 \vec{AB}=0\hat{i}+2\hat{j}+0\hat{k}

\vec{AC}=\hat{i}+2\hat{j}+2\hat{k}

\vec{AD}=-\hat{i}+3\hat{j}+2\hat{k}

\therefore Volume of tetrahedron 

=\left | \frac{1}{6}\begin{vmatrix} 0 &2 &0 \\ 1&2 &2 \\ -1 &3 &2 \end{vmatrix} \right |

=\left | \frac{1}{6}(-2)(4) \right |=\frac{4}{3} (unit)^{3}

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vinayak

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