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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
Question
Choose the correct answer from the given four options.
The value of $\lambda$ for which the vectors $3\hat{\text{i}}-6\hat{\text{j}}+\hat{\text{k}}$ and $2\hat{\text{i}}-4\hat{\text{j}}+\lambda\hat{\text{k}}$ are parallel, is:
  1. $\frac{2}{3}$
  2. $\frac{3}{2}$
  3. $\frac{5}{2}$
  4. $\frac{2}{5}$
✓

Answer

  1. $\frac{2}{3}$

Solution:

As the vectors $3\hat{\text{i}}-6\hat{\text{j}}+\hat{\text{k}}$ and $2\hat{\text{i}}-4\hat{\text{j}}+\lambda\hat{\text{k}}$ are parallel

$\therefore\frac{3}{2}=\frac{-6}{-4}=\frac{1}{\lambda}$

$\Rightarrow\lambda=\frac{2}{3}$

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