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  2. Find the vector equation of the line which passes through the point (3, 4, 5) and is parallel to the vector
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Find the vector equation of the line which passes through the point (3, 4, 5) and is parallel to the vector 2\hat{i}+2\hat{j}-3\hat{k}. 

 

 

 

 
 
 
 
 

Answers (1)
R Ravindra Pindel

Given the line passes through a point  (3,4,5)  and parallel to vector   2\hat{i}+2\hat{j}-3\hat{k}

Direction ratios are (2,2,-3)

\therefore  Vector equation of the line :  \vec{r}=\vec{a}+\lambda \vec{b}

\vec{b}=2\hat{i}+2\hat{j}-3\hat{k}

\vec{a}=3\hat{i}+4\hat{j}+5\hat{k}

\therefore \vec{r}=(3\hat{i}+4\hat{j}+5\hat{k})+\lambda (2\hat{i}+2\hat{j}-3\hat{k})

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