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  • I have a doubt, kindly clarify. - Three Dimensional Geometry - JEE Main-2

Let lines l_{1} , l_{2} are in direction of \vec{a} and \vec{b} respectively which of the following pairs of \vec{a} & \vec{b} represents l_{1} & l_{2} are parallel 

  • Option 1)

    \hat{i}-2\hat{j}+\hat{k}, \hat{i}-\hat{j}+\hat{k}

  • Option 2)

    \hat{i}+\hat{j}-\hat{k}, 2\hat{i}+\hat{j}-2\hat{k}

  • Option 3)

    -2\hat{i}+2\hat{j}-2\hat{k}, \hat{i}-\hat{j}-\hat{k}

  • Option 4)

    \frac{2}{3}\hat{i}-\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}, -\hat{i}+\hat{j}-\hat{k}

 

Answers (1)

best_answer

As we have learned

Condition of Parallelism -

Two lines will be Parallel if

\vec{b}= \lambda \vec{b_{1}}     or   \frac{a_{1}}{a_{2}}= \frac{b_{1}}{b_{2}}= \frac{c_{1}}{c_{2}}

-

 

 (D) is the only option where \vec{b}=\lambda\vec{a} is followed

 we can see that

-\hat{i}+\hat{j}-\hat{k }=\frac{-3}{2}(\frac{2}{3}\hat{i}-\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k})

\therefore Option D


Option 1)

\hat{i}-2\hat{j}+\hat{k}, \hat{i}-\hat{j}+\hat{k}

Option 2)

\hat{i}+\hat{j}-\hat{k}, 2\hat{i}+\hat{j}-2\hat{k}

Option 3)

-2\hat{i}+2\hat{j}-2\hat{k}, \hat{i}-\hat{j}-\hat{k}

Option 4)

\frac{2}{3}\hat{i}-\frac{2}{3}\hat{j}+\frac{2}{3}\hat{k}, -\hat{i}+\hat{j}-\hat{k}

Posted by

Himanshu

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