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STD 12 - 10. vector algebra — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 10. vector algebra4 Marks
MCQ
Volume of a parallelepiped with coterminous edges $\vec a, \vec b, \vec c$ is $12\, cu$ units. Volume of a tetrahedron with coterminous edges $ \vec a - \vec b, \vec b - \vec c, \vec a + \vec b - \vec c$ will be - ............. $\mathrm{cu\, uints}$
  • ✓
    $2$
  • B
    $3$
  • C
    $6$
  • D
    $12$
✓

Answer

Correct option: A.
$2$
a
$[\vec{a} \vec{b} \vec{c}]=12$

$\frac{1}{6}\left(\left[\begin{array}{ccc}{\vec{a}-\vec{b}} & {\vec{b}-\vec{c}} & {\vec{a}-\vec{c}+\vec{b}}\end{array}\right]\right)=\frac{1}{6}[\vec{a} \vec{b} \vec{c}]=2$

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