Show that the vectors $2\hat i - 3\hat j + 4\hat k$ and $- 4\hat i + 6\hat j - 8\hat k$ are collinear.

Let $\vec a = 2\hat i - 3\hat j + 4\hat k$ and $\vec b = - 4\hat i + 6\hat j - 8\hat k$
Now, $\vec b = - 2(2\hat i - 3\hat j + 4\hat k) = - 2\vec a$

$\Rightarrow \vec b$ is a scalar multiple of $\vec a \Rightarrow \vec a$ and $\vec b$ have same direction.
Hence, $\vec a$ and $\vec b$ are collinear.