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VECTOR ALGEBRA — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVECTOR ALGEBRA1 Mark
Question
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:
  1. $\frac{1}{3}$
  2. $3$
  3. $-3$
  4. $\frac{-1}{3}$
✓

Answer

  1. $\frac{1}{3}$
Solution:
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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