Q95 / 180 · KCET 2019 · Mathematics

\( [\vec{a}+2 \vec{b}-\vec{c}, \vec{a}-\vec{b}, \vec{a}-\vec{b}-\vec{c}]= \)

  • A
    \( [\vec{a}, \vec{b}, \vec{c}] \)
  • Correct answer
    B
    \( 3[\vec{a}, \vec{b}, \vec{c}] \)
  • C
    \( 00 \)
  • D
    \( 2[\vec{a}, \vec{b}, \vec{c}] \)

Solution

(B) \( (\vec{a}+2 \vec{b}-\vec{c}) \cdot\{\vec{a}-\vec{b} \times \vec{a}-\vec{b}-\vec{c}\} \) \( =(\vec{a}+2 \vec{b}-\vec{c}) \cdot\{-\vec{a} \times \vec{b}-\vec{a} \times \vec{c}-\vec{b} \times \vec{a}+\vec{b} \times \vec{c}\} \) \( =[\vec{a} \vec{b} \vec{c}]-2[\vec{b} \vec{a} \vec{c}] \) \( =[\vec{a} \vec{b} \vec{c}]+2[\vec{a} \vec{b} \vec{c}] \) \( =3[\vec{a} \vec{b} \vec{c}] \)

Hence, the correct answer is option: 'B'.

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