Question

If ` vec r_1, vec r_2, vec r_3` are the position vectors off thee collinear points and scalar `pa n dq` exist such that ` vec r_3=p vec r_1+q vec r_2,` then show that `p+q=1.`

Answer 1

`vec(r_3)= p vec(r_1)+q (r_2)`
`" "=(pvec(r_1)+ (1-p)vec(r_2))/(p+ (1+p))`
`vec(r_3)` divides `vec(r_1)` in the ratios `(1-p): p`
Hence, `vec(r_1), vec(r_2) and vec(r_3)` are collinear.