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