Question
If two vectors $2\hat i + 3\hat j - \hat k$ and $ - 4\hat i - 6\hat j + \lambda \hat k$ are parallel to each other then value of $\lambda$ be
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Answer
(b) Let $\overrightarrow A = 2\hat i + 3\hat j - \hat k$ and $\overrightarrow B = - 4\hat i - 6\hat j + \lambda \hat k$
$\overrightarrow A $ and $\overrightarrow B $ are parallel to each other
$\frac{{{a_1}}}{{{b_1}}} = \frac{{{a_2}}}{{{b_2}}} = \frac{{{a_3}}}{{{b_3}}}$ i.e. $\frac{2}{{ - 4}} = \frac{3}{{ - 6}} = \frac{{ - 1}}{\lambda }$$ \Rightarrow \,\,\lambda = 2$.
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