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  • Help me please, - Three Dimensional Geometry - JEE Main-4

Which of the following lines is parallel to (\hat{i}-\hat{j}+\hat{k})

  • Option 1)

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

  • Option 2)

    \vec{r}=(1+\lambda)\hat{i}+ (3-\lambda)\hat{j}+ (2+\lambda)\hat{k}

  • Option 3)

    \vec{r}=\lambda\hat{i}+ -2\lambda\hat{j}+ (1+\lambda)\hat{k}

  • Option 4)

    None of these

 

Answers (1)

best_answer

As we have learned

Vector equation of a line -

The equation of a line passing through A\left ( \bar{a}\right )and parallel to vector \vec{b} is given by

\vec{r}= \vec{a}+\lambda \vec{b}  .

The equation of a line passing through two points A\left ( \vec{a} \right )\, and \, B\left ( \vec{b} \right )\, is given by

\vec{r}= \vec{a}+\lambda \left ( \vec{b}-\vec{a} \right )

 

- wherein

 

 Option (A) will be \vec{r}=(2\hat{i}+3\hat{j}+4\hat{k}) + \lambda(\hat{i}-\hat{j}+2\hat{k}) 

Option (B) will be \vec{r}=(\hat{i}+3\hat{j}+2\hat{k}) + \lambda(\hat{i}-\hat{j}+\hat{k})

Option (C) will be \vec{r}=(\hat{k}) + \lambda(\hat{i}-2\hat{j}+\hat{k})

we see line in (B) has direction parallel to \hat{i}-\hat{j}+\hat{k}

\therefore Option (B)


Option 1)

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

Option 2)

\vec{r}=(1+\lambda)\hat{i}+ (3-\lambda)\hat{j}+ (2+\lambda)\hat{k}

Option 3)

\vec{r}=\lambda\hat{i}+ -2\lambda\hat{j}+ (1+\lambda)\hat{k}

Option 4)

None of these

Posted by

Himanshu

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