Question

Show that the point P,Q and Rwith position vectors
a - 3b + c, -2a +3b + 4c, -b+2c are collinear

Answer 1

Vectors are colinear if they are multiples of eac other so let's take a look
\[a-3b+c\]\[-2a+3b+4c\]\[-b+2c\]
so see if you can multiply one of them by another constant and get them. Essentially look for a directional vector that can get you to each of the point from each of the others

Answer 2

I think P,Q,R is co-linear if,

P-Q=t(R-Q)

$$P-Q=(a-3b+c)-(-2a+3b+4c)=3(a-2b-c)$$
$$R-Q=(-b+2c)-(-2a+3b+4c)=2(a-2b-c)$$

It is clear that $$(P-Q)=\frac{3}{2}(R-Q)$$
so these points are colinear