The lines{r}=({i}-{j})+l(2{i}+{k}) and{r}=(2{i}-{j})+m({i}+{j}-{k}) [3 Sep 2020 Shift 1]

Correct Answer is : Do not intersect for any values of lll and mmm

Intersect for all values of l and m

Correct Answer is : Do not intersect for any values of lll and mmm

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JEE Mains 03 Sep 2020 Shift 1 Solved Paper

Section: Mathematics

Question : 52 of 75

Marks: +1, -0

The lines

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

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

Solution:

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

+\hat{k}(l)

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

+\hat{k}(-m)

For intersection

1+2l=2+m

...... (i)

-1=m-1

...... (ii)

l=-m

...... (iii)

from (ii) m = 0

from (iii)l = 0

These values of

m

and

l

do not satisfyequation (1)

Hence the two lines do not intersect for anyvalues of

l

and

m

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