A) \[\frac{1}{3}\]cubic unit
B) \[\frac{1}{4}\]cubic unit
C) \[\frac{2}{5}\]cubic unit
D) \[\frac{2}{3}\]cubic unit
Correct Answer: D
Solution :
Idea \[\because \] OABC is a tetrahedron, where OA = a, OB = b, OC = c, OD = d \[V=\frac{1}{6}[abc]=\left| \frac{1}{6}\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|\,\,\,\, \right|\] We know that volume of tetrahedron is \[=\frac{1}{6}\left| \begin{matrix} 3 & 4 & 2 \\ 0 & 4 & 1 \\ 1 & 0 & 0 \\ \end{matrix} \right|\]Solving this, we get \[V=\frac{2}{3}\]cubic unit TEST Edge Generally, in JEE Main geometrical application of vector triple product such as the vectors are coplanar related questions are asked. To solve these types of questions, students are advised to understand the concept of vector triple product.
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