(Solved):   Please help Consider the linear combination of the position vectors of the points \( P_{1} ...

 

Please help

Consider the linear combination of the position vectors of the points \( P_{1} \) and \( P_{2} \) : \[ \vec{r}_{3}=a \vec{r}_{1}+b \vec{r}_{2} \] for any combination of the variables \( a \) and \( b \) for which \( a+b=1 \) Proof that the above linear combination of the two position vectors is itself the position vector of a point that lies on the line connecting the original points \( P_{1} \) and \( P_{2} \).