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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
The unit vector perpendicular to $3i + 2j - k$ and $12i + 5j - 5k,$ is
  • A
    $\frac{{5i - 3j + 9k}}{{\sqrt {115} }}$
  • B
    $\frac{{5i + 3j - 9k}}{{\sqrt {115} }}$
  • ✓
    $\frac{{ - 5i + 3j - 9k}}{{\sqrt {115} }}$
  • D
    $\frac{{5i + 3j + 9k}}{{\sqrt {115} }}$
✓

Answer

Correct option: C.
$\frac{{ - 5i + 3j - 9k}}{{\sqrt {115} }}$
c
(c) $a \times b = \left| {\begin{array}{*{20}{c}}i&j&k\\3&2&{ - 1}\\{12}&5&{ - 5}\end{array}} \right| = - 5\,i + 3j - 9k.$

Unit vector along $a \times b = \frac{{ - 5i + 3j - 9k}}{{\sqrt {115} }}.$

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