• question_answer The volume of tetrahedron with one of the vertex at origin and the others 3 at points A (3, 4, 2) B (0, 4, 1) and C (1, 0, 0) is A)  $\frac{1}{3}$cubic unit               B)  $\frac{1}{4}$cubic unit            C)  $\frac{2}{5}$cubic unit               D)  $\frac{2}{3}$cubic unit

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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