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  • Let the vectors  represent three coterminous edges of a

Let the vectors \vec{a},\vec{b},\vec{c} represent three coterminous edges of a parallelepiped of volume V. Then the volume of the parallelepiped, whose coterminous edges are represented by \vec{a},\vec{b}+\vec{c} and \vec{a}+2\vec{b}+3\vec{c}is equal to :

Option: 1

2V


Option: 2

6V


Option: 3

3V


Option: 4

V


Answers (1)

best_answer

\begin{aligned} & \mathrm{v}_1=\left[\begin{array}{lll} \overrightarrow{\mathrm{a}} & \vec{b}+\overrightarrow{\mathrm{c}} & \overrightarrow{\mathrm{a}}+2 \vec{b}+3 \vec{c} \end{array}\right] \\ & \mathrm{v}_1=\left|\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 2 & 3 \end{array}\right|[\vec{a} \vec{b} \vec{c}] \\ & \mathrm{v}_1=(3-2) \mathrm{v} \\ & =\mathrm{V} \\ & \end{aligned}

Correct Answer is Option 4

Posted by

sudhir.kumar

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