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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
If the vectors $2i - j + k,\,\,i + 2j - 3k$ and $3i + \lambda j + 5k$ be coplanar, then $\lambda = $
  • A
    $-1$
  • B
    $-2$
  • C
    $-3$
  • ✓
    $-4$
✓

Answer

Correct option: D.
$-4$
d
(d) If the given vectors are coplanar, then their scalar triple product is zero.

$\left| {\begin{array}{*{20}{c}}2&{ - 1}&1\\1&2&{ - 3}\\3&\lambda &5\end{array}} \right| = 0 \Rightarrow \lambda = - 4.$

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