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STD 12 - 10. vector algebra — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 10. vector algebra1 Mark
MCQ
$|a \times i{|^2} + |a \times j{|^2} + |a \times k{|^2} = $
  • A
    $|a{|^2}$
  • ✓
    $2\,\,|a{|^2}$
  • C
    $3\,\,|a{|^2}$
  • D
    $4\,\,|a{|^2}$
✓

Answer

Correct option: B.
$2\,\,|a{|^2}$
b
(b) $|a \times i{|^2} = {\left| {\begin{array}{*{20}{c}}i&j&k\\{{a_1}}&{{a_2}}&{{a_3}}\\1&0&0\end{array}} \right|^2}$, $({\rm{Since}}\,\,\,a = {a_1}i + {a_2}j + {a_3}k)$

$ = \,|{a_3}j - {a_2}k{|^2} = a_3^2 + a_2^2$

Similarly, $|a \times j{|^2} = a_1^2 + a_3^2$ and $|a \times k{|^2} = a_1^2 + a_2^2$

Hence the required result can be given as

$2(a_1^2 + a_2^2 + a_3^2) = 2|a{|^2}.$

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