Q. The vector equation of the line passing through the points $(3,2,1)$ and $( - 2,1,3)\$is
A) $\overrightarrow{\mathbf{r}} = 3\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}} + \ \lambda( - 5\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}})$
B) $\overrightarrow{\mathbf{r}} = 3\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}} + \ \lambda( - 5\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}})$
C) $\overrightarrow{\mathbf{r}} = - 2\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + 3\widehat{\mathbf{k}} + \ \lambda(5\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}})$
D) $\overrightarrow{\mathbf{r}} = - 2\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}} + \ \lambda(5\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}})$
Explanation
(a)
The vector equation of line passing through points (3, 2, 1) and $( - 2,\ 1,\ 3)$
$\overrightarrow{\mathbf{r}} = 3\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}} + \lambda\left\lbrack ( - 2 - 3)\widehat{\dot{\mathbf{i}}} + (1 - 2)\widehat{\dot{\mathbf{j}}} + (3 - 1)\widehat{\mathbf{k}} \right\rbrack$
$= 3\widehat{\dot{\mathbf{i}}} + 2\widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}} + \lambda( - 5\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + 2\widehat{\mathbf{k}}$)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.