Question

The vector equation of the line passing through the points $(3,2,1)$ and $(-2,1,3)$ is

• A. $\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}-\hat{j}+2\hat{k})$
• B. $\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}+\hat{j}+\hat{k})$
• C. $\vec{r}=-2\hat{i}+\hat{j}+3\hat{k}+\lambda (5\hat{i}+\hat{j}+2\hat{k})$
• D. $\vec{r}=-2\hat{i}+\hat{j}+\hat{k}+\lambda (5\hat{i}+\hat{j}+2\hat{k})$

Answer 1

Answer: (A)

$\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}-\hat{j}+2\hat{k})$

Answer 2

The correct option is(A): $\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}-\hat{j}+2\hat{k})$

The vector equation of a line passing through $(3,2,1)$ and $(-2,1,3)$ is $\vec{r}=3\hat{i}+2\hat{j}+\hat{k}+\lambda [(-2-3)\hat{i}+(1-2)\hat{j}$
$+(3-1)\hat{k}]$ $=3\hat{i}+2\hat{j}+\hat{k}+\lambda (-5\hat{i}-\hat{j}+2\hat{k})$