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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
If $x\,.\,a = 0,\,\,x\,.\,b = 0$ and $x\,.\,c = 0$ for some non-zero vector $x$, then the true statement is
  • ✓
    $[a\,\,b\,\,c] = 0$
  • B
    $[a\,\,b\,\,c] \ne 0$
  • C
    $[a\,\,b\,\,c] = 1$
  • D
    None of these
✓

Answer

Correct option: A.
$[a\,\,b\,\,c] = 0$
a
(a) Since $x$is a non-zero vector, the given conditions will be satisfied, if either $(i)$ at least one of the vectors $a,\,\,b,\,\,c$ is zero or $(ii)$ $x$ is perpendicular to all the vectors $a,\,\,b,\,\,c.$

In case $(ii),$ $a,\,\,b,\,\,c$ are coplanar and so $[a\,\,b\,\,c] = 0.$

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