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Vector Algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector Algebra1 Mark
MCQ
If vectors $(\text{x}-2)\ \vec{\text{a}}+\vec{\text{b}}$ and $(2\text{x}+1)\ \vec{\text{a}}-\vec{\text{b}}$ are parallel then $x:$
  • ✓
    $\frac{1}{3}$
  • B
    $3$
  • C
    $-3$
  • D
    $\frac{-1}{3}$
✓

Answer

Correct option: A.
$\frac{1}{3}$
As vectors $(x - 2) a + b$ and $(2x + 1) a - b$ are parallel.
$\frac{\text{x}-2}{2\text{x}+1}=-1$
$\Rightarrow\text{x} - 2=-2\text{x}-1$
$\therefore\text{x}=\frac{1}{3}$

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