Show that the three vectors $$A\_ = 2i + j - 3k , B\_ = i - 4k , C\_ = 4i + 3j -k$$ are linearly dependent. Determine a relation between them and hence show that the terminal points are collinear.
Here in this question I proved the first part. But how can I show that the terminal points are collinear?
You would find a single line through the points $(2,1,-3), (1,0,-4), (4,3-1)$. One way would be to take $B-A$ and $C-A$ and show they are proportional. That would say you can represent $C$ as $A+t(B-A)$ Clearly you can represent $A,B$ that way with $t=0,1$