JEE Main & Advanced
Mathematics
Vector Algebra
Question Bank
Critical Thinking
question_answer
The volume of the tetrahedron, whose vertices are given by the vectors \[-\mathbf{i}+\mathbf{j}+\mathbf{k},\,\,\mathbf{i}-\mathbf{j}+\mathbf{k}\] and \[\mathbf{i}+\mathbf{j}-\mathbf{k}\]with reference to the fourth vertex as origin, is
A)\[\frac{5}{3}\]cubic unit
B)\[\frac{2}{3}\] cubic unit
C)\[\frac{3}{5}\]cubic unit
D)None of these
Correct Answer:
B
Solution :
Volume of tetrahedron \[ABCD\] is, \[\frac{1}{6}|\overrightarrow{AB}\times \overrightarrow{AC}\,.\,\overrightarrow{AD}|\], where \[A(-1,\,1,\,1),\] \[B(1,\,-1,\,1),\] \[C(1,\,1,\,-1)\] and \[D(0,\,0,\,0).\]