# The number of distinct real values of λ for which the lines andare coplanar is : Option 1) 4 Option 2) 1 Option 3) 2 Option 4) 3

As we learnt in

Condition for lines to be intersecting (cartesian form) -

Their shortest distance should be 0

Also the condition for coplanar lines

-

For two lines to be coplanar

$[a^{-1}-b^{-1}\, \, \, \, \, \, r_{1}^{-1}\, \, \, \, \, r_{2}^{-1}]=0$

$\begin{vmatrix} 2 & 0&4 \\ 1 &2 &\lambda^{2} \\ 1 & \lambda^{2} & 2 \end{vmatrix}=0$

$2(4-\lambda^{4})+4(\lambda^{2}-2)=0$

$\lambda^{4}=2\lambda^{2}$

$\lambda^{4}-2\lambda^{2}=0$

$\lambda^{2}(\lambda^{2}-2)=0$

But $\lambda\pm 0\: \therefore \lambda=\pm \sqrt{2}$

Two values of $\lambda$ are possible

Option 1)

4

This option is incorrect

Option 2)

1

This option is incorrect

Option 3)

2

This option is correct

Option 4)

3

This option is incorrect

### Preparation Products

##### JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
##### Knockout JEE Main April 2021 (Easy Installments)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
##### Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
##### Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-