Find the position vector of point C which divides the line segment joining points A and B having position vectors i +2 j - k and - i + j + k…

Position vector of $\displaystyle C=\vec{r}=\frac{4 \vec{b}-\vec{a}}{3}$ $$\text { i.e. } \vec{r}=\frac{1}{3}(-5 \hat{i}+2 \hat{j}+5 \hat{k}) $$ Now, $\displaystyle \overrightarrow{A B}=-2 \hat{i}-\hat{j}+2 \hat{k} \Rightarrow|\overrightarrow{A B}|=3$ $$\overrightarrow{B C}=-\frac{1}{3}(2 \hat{i}+\hat{j}-2 \hat{k}) \Rightarrow|\overrightarrow{B C}|=1 $$ $\displaystyle |\overrightarrow{A B}|:|\overrightarrow{B C}|=3: 1$