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Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
MCQ
The volume of parallelopiped with vector $\bar{a}+2 \bar{b}-\bar{c}, \bar{a}-\bar{b}$ and $\bar{a}-\bar{b}-\bar{c}$ is equal to $k[\bar{a} \bar{b} \bar{c}]$, then $k=$
  • A
    $-3$
  • ✓
    3
  • C
    2
  • D
    $-2$
✓

Answer

Correct option: B.
3
(B) Volume of parallelopiped
$=\left|\begin{array}{ccc}1 & 2 & -1 \\ 1 & -1 & 0 \\ 1 & -1 & -1\end{array}\right|[\overline{ a } \overline{ b } \overline{ c }]= k [\overline{ a } \overline{ b } \overline{ c }]$
$\begin{array}{l}\Rightarrow 1(1-0)-2(-1-0)-1(-1+1)= k \\ \Rightarrow 1+2-0= k \Rightarrow k =3\end{array}$

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