Choose the correct answer from the given four options. The value … - Vidyadip

MCQ

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:

✓
$\frac{2}{3}$
B
$\frac{3}{2}$
C
$\frac{5}{2}$
D
$\frac{2}{5}$

✓

Answer

Correct option: A.

$\frac{2}{3}$

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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