Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Find the vector equation of a line passing through the point   and parallel to the line <img alt="\vec{r}=

Find the vector equation of a line passing through the point \left ( 2,3,2 \right )  and parallel to the line \vec{r}= \left ( -2\hat{i}+3\hat{j} \right )+\lambda \left ( 2\hat{i}-3\hat{j}+6\hat{k} \right ). Also ,find the distance between these two lines.

 

 

 

 
 
 
 
 

Answers (1)

As the d.r's of parallel lines are proportional so,the equation of line passing through \left ( 2,3,2 \right )  and parallel to \vec{r}= \left ( -2\hat{i}+3\hat{j} \right )+\lambda \left ( 2\hat{i}-3\hat{j}+6\hat{k} \right ) is:
                      \vec{r}= \left ( 2\hat{i}+3\hat{j}+2\hat{k} \right )+\lambda \left ( 2\hat{i}-3\hat{j}+6\hat{k} \right )
       Now  \vec{a_{1}}= -2\hat{i}+3\hat{j},\vec{a_{2}}= 2\hat{i}+3\hat{j}+2\hat{k}
                \vec{b_{1}}= 2\hat{i}-3\hat{j}+6\hat{k}
     \Rightarrow \vec{a_{2}}-\vec{a_{1}}= \left ( 2\hat{i}+3\hat{j}+2\hat{k} \right )-\left ( -2\hat{i}+3\hat{j} \right )= 4\hat{i}+2\hat{k}
          and\Rightarrow \left (\vec{a_{2}}-\vec{a_{1}} \right )\times \vec{b}= \begin{vmatrix} \hat{i} & \hat{j} &\hat{k} \\ 4 & 0 & 2\\ 2& -3 & 6 \end{vmatrix}
                                                = 6\hat{i}-20\hat{j}-12\hat{k}   
           \therefore SD= \frac{\left | \left ( \vec{a_{2}}-\vec{a_{1}} \right )\times \vec{b} \right |}{\left | \vec{b} \right |}
\Rightarrow \frac{\left | 6\hat{i}-20\hat{j}-12\hat{k} \right |}{\left | 2\hat{i}-3\hat{j}+6\hat{k} \right |}\Rightarrow \frac{\sqrt{36+400+144}}{\sqrt{4+9+36}}
\Rightarrow \frac{\sqrt{580}}{7} units

Posted by

Ravindra Pindel

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Board Result 2025 LIVE: Class 10th, 12th results by next week; DigiLocker codes, latest updates
anam-khan

Fake notice on CBSE 10th, 12th results 2025 in two-halves viral, board alerts students
anam-khan

CBSE Board Result 2025 LIVE: Class 10th, 12th results on cbse.nic.in soon; pass marks, DigiLocker code

Latest Question