Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2 i caret - j caret + 4 caret and is in the direction i caret + 2 j caret - k caret.

5. Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2\widehat{i}-\widehat{j}+4\widehat{k}and is in the direction  \widehat{i}+2\widehat{j}-\widehat{k}.

Answers (1)

best_answer

Given that the line is passing through the point with position vector 2\widehat{i}-\widehat{j}+4\widehat{k} and is in the direction of the line \widehat{i}+2\widehat{j}-\widehat{k}.

And we know the equation of the line which passes through the point with the position vector \vec{a}and parallel to the vector \vec{b} is given by the equation,

\vec{r} = \vec{a} +\lambda\vec{b}

\Rightarrow \vec{r} =2\widehat{i}-\widehat{j}+4\widehat{k} + \lambda(\widehat{i}+2\widehat{j}-\widehat{k})

So, this is the required equation of the line in the vector form.

\vec{r} =x\widehat{i}+y\widehat{j}+z\widehat{k} = (\lambda+2)\widehat{i}+(2\lambda-1)\widehat{j}+(-\lambda+4)\widehat{k}

Eliminating \lambda, from the above equation we obtain the equation in the Cartesian form :

\frac{x-2}{1}= \frac{y+1}{2} =\frac{z-4}{-1}

Hence this is the required equation of the line in Cartesian form.

Posted by

Divya Prakash Singh

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 Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years
anam-khan

CBSE Class 12 accountancy board exam analysis 2024 out; paper rated easy, balanced

Latest Question