A) \[(13,-8,\,7)\]
B) \[(4,-3,\,5)\]
C) \[(-14,7,\,6)\]
D) \[(22,-13,12)\]
Correct Answer: D
Solution :
Given, straight line is \[\vec{r}=(-5\hat{i}+2\hat{j}+3\hat{k})+\,t\,(9\hat{i}-5\hat{j}+3\hat{k})\] which is the line passing through the point \[-5\hat{i}+2\hat{j}+3\hat{k}\] and parallel to the vector \[9\hat{i}-5\hat{j}+3\hat{k}\]. From the options taking option \[(22,-13,12)\] Let \[\vec{a}=-5\hat{i}+2\hat{j}+3\hat{k}\] \[\vec{c}=22\hat{i}-13\hat{j}+12\hat{k}\] \[\overrightarrow{AC}=\vec{c}-\vec{a}\] \[=(22\hat{i}-13\hat{j}+12\hat{k})-(-5\hat{i}+2\hat{j}+3\hat{k})\] \[=27\hat{i}-15\hat{j}+9\hat{k}\] \[=3(9\hat{i}-5\hat{j}+3\hat{k})\] which is parallel to vector \[\vec{b}\,(9\hat{i}-5\hat{j}+3\hat{k})\]. Thus, we have shown that \[\overrightarrow{AC}\] is parallel to \[\vec{b}\]. Hence, \[\vec{c}\] lies on the given line. Hence, option is correct.
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