b
(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. \(\frac{2}{{ - 4}} = \frac{3}{{ - 6}} = \frac{{ - 1}}{\lambda }\)\( \Rightarrow \,\,\lambda = 2\).