Show that the lines and are coplanar. Also find the equation of the plane containing these lines.

Given : Equations of lines –

Line 1 :

Line 2 :

To Prove : Line 1 & line 2 are coplanar.

To Find : Equation of plane.

Formulae :

1) Coplanarity of two lines :

If two lines are given by,

and

, then these lines are coplanar, if

2) Equation of plane :

The equation of plane containing two coplanar lines

& is given by,

Answer :

Given lines –

Line 1 :

Line 2 :

Here, x₁ = 1 , y₁ = 3 , z₁ = 0 , a₁ = 2 , b₁ = -1 , c₁ = -1

x₂ = 4 , y₂ = 1 , z₂ = 1 , a₂ = 3 , b₂ = -2 , c₂ = -1

Now,

= - 2

Hence, given two lines are not coplanar.