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Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
MCQ
$(\bar{a}+\bar{b}) \cdot(\bar{b}+\bar{c}) \times(\bar{a}+\bar{b}+\bar{c})=$
  • A
    -$[\bar{a} \bar{b} \bar{c}]$
  • ✓
    $[\bar{a} \bar{b} \bar{c}]$
  • C
    $0$
  • D
    $2[\overline{ a } \overline{ b } \overline{ c }]$
✓

Answer

Correct option: B.
$[\bar{a} \bar{b} \bar{c}]$
(B) $(\overline{ a }+\overline{ b }) \cdot(\overline{ b }+\overline{ c }) \times(\overline{ a }+\overline{ b }+\overline{ c })$
$=(\overline{ a }+\overline{ b }) \cdot[\overline{ b } \times \overline{ a }+\overline{ b } \times \overline{ c }+\overline{ c } \times \overline{ a }+\overline{ c } \times \overline{ b }]$
$=[\overline{ a } \overline{ b } \overline{ a }]+[\overline{ a } \overline{ b } \overline{ c }]+[\overline{ a c a }]+[\overline{ a c} \overline{b}]$ $+[\overline{ b } \overline{ b } \overline{ a }]+[\overline{ b } \overline{ b } \overline{ c }]+[\overline{ b } \overline{ c } \overline{ a }]+[\overline{ b } \overline{ c } \overline{ b }]$
$=0+[\overline{ a } \overline{ b } \overline{ c }]+0+[\overline{ a } \overline{ c } \overline{ b }]+0+0+[\overline{ b } \overline{ c } \overline{ a }]+0$
$=[\overline{ a } \overline{ b } \overline{ c }]-[\overline{ a } \overline{ b } \overline{ c }]+[\overline{ a } \overline{ b } \overline{ c }]=[\overline{ a } \overline{ b } \overline{ c }]$

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