question_answer

The volume of the tetrahedron the p. v' s of whose angular points are (5, 2, -3), (11, 2, 3), (5, 8, 3) and (5, 2, 3) is

A) 6                                             

B) 36

C) 72                                          

D) 12

Correct Answer: B

Solution :

Volume \[=\left| \frac{1}{6}\overline{AB},\,\,\overline{BC},\,\,\overline{CD} \right|\] \[\overline{AD}=-6\widehat{k},\,\,\overline{BD}=6\widehat{i},\,\,\overline{CD}=6\widehat{j}\] \[\therefore \]\[V=\frac{1}{6}\times 216[\widehat{i}\,\,\widehat{j}\,\,\widehat{k}]\]                         \[=36\]