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Question Bank [2022] — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsQuestion Bank [2022]2 Marks
Question
If $\overline{ c }=3 \overline{ a }-2 \overline{ b }$ then prove that $\left[\begin{array}{lll}\overline{ a } & \overline{ b } & \overline{ c }\end{array}\right]=0$
✓

Answer

$\bar{c}=3 \bar{a}-2 \bar{b}$
$[$Given$]$
$\begin{array}{l}{\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]=\bar{a} \cdot(\bar{b} \times \bar{c})}\end{array} $
$=\bar{a} \cdot[\bar{b} \times(3 \bar{a}-2 \bar{b})] $
$=\bar{a} \cdot[\bar{b} \times 3 \bar{a}-\bar{b} \times 2 \bar{b}] $
$=\bar{a} \cdot[\bar{b} \times 3 \bar{a}-\overline{0}] \quad \ldots \ldots \ldots \cdot[\because \bar{b} \times \bar{b}=\overline{0}] $
$=3 \bar{a} \cdot[\bar{b} \times \bar{a}] $
$=3\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{a} \end{array}\right] $
$=3(0) $
$\therefore\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{a}\end{array}\right]=0$

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