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Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
MCQ
$[\bar{a}+2 \bar{b}-\bar{c} \quad \bar{a}-\bar{b} \quad \bar{a}-\bar{b}-\bar{c}]=$
  • A
    $\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]$
  • ✓
    $3\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]$
  • C
    $0$
  • D
    $2\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]$
✓

Answer

Correct option: B.
$3\left[\begin{array}{lll}\bar{a} & \bar{b} & \bar{c}\end{array}\right]$
(B) $[\overline{ a }+2 \overline{b}-\overline{ c } \quad \overline{ a }-\overline{ b } \quad \overline{ a }-\overline{ b }-\overline{ c }]$
$=(\overline{ a }+2 \overline{b}-\overline{ c }) \cdot\{(\overline{ a }-\overline{ b }) \times(\overline{ a }-\overline{ b }-\overline{ c })\}$
$=(\overline{ a }+2 \overline{b}-\overline{ c })$ $\cdot\{\overline{ a } \times \overline{ a }-\overline{ a } \times \overline{ b }-\overline{ a } \times \overline{ c }-\overline{ b } \times \overline{ a }+\overline{ b } \times \overline{ b }+\overline{ b } \times \overline{ c }\}$
$=(\overline{ a }+2 \overline{b}-\overline{ c })\{\overline{ b } \times \overline{ a }-\overline{ a } \times \overline{ c }-\overline{ b } \times \overline{ a }+\overline{ b } \times \overline{ c }\}$
$=(\overline{ a }+2 \overline{b}-\overline{ c })\{-\overline{ a } \times \overline{ c }+\overline{ b } \times \overline{ c }\}$
$\begin{array}{l}=\left[\begin{array}{lll}\overline{ a } & \overline{ b } & \overline{ c }\end{array}\right]-2\left[\begin{array}{lll}\overline{ b } & \overline{ a } & \overline{ c }\end{array}\right] \\ =\left[\begin{array}{lll}\overline{ a } & \overline{ b } & \overline{ c }\end{array}\right]+2\left[\begin{array}{lll}\overline{ a } & \overline{ b } & \overline{ c }\end{array}\right] \\ =3\left[\begin{array}{lll}\overline{ a } & \overline{ b } & \overline{ c }\end{array}\right]\end{array}$

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