A) \[\overrightarrow{r}=\overrightarrow{a}+\overrightarrow{b}\]
B) \[\overrightarrow{r}=\overrightarrow{a}+t(\overrightarrow{b}-\overrightarrow{a})\]
C) \[\overrightarrow{r}=\overrightarrow{a}+t\overrightarrow{b}\]
D) None of these
Correct Answer: B
Solution :
\[\overrightarrow{a}={{a}_{1}}\hat{i}+{{a}_{2}}\hat{j}+{{a}_{3}}\hat{k}\] and \[\overrightarrow{b}={{b}_{1}}\hat{i}+{{b}_{2}}\hat{j}+{{b}_{3}}\hat{k}\] The line passing through\[\overrightarrow{a}\]and\[\overrightarrow{b}\]is \[\overrightarrow{r}=\overrightarrow{a}(1-t)+t\overrightarrow{b}\] Or \[\overrightarrow{r}=\overrightarrow{a}(\overrightarrow{b}-\overrightarrow{a})t\]
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