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 = -2 , a₁ = -3 , b₁ = 2 , c₁ = 1

x₂ = 0 , y₂ = 7 , z₂ = -7 , a₂ = 1 , b₂ = -3 , c₂ = 2

Now,

= 7 + 28 – 35

= 0

Hence, given two lines are coplanar.

Equation of plane passing through line1 and line 2 is given by,

7x + 7 + 7y – 21 + 7z + 14 = 0

7x + 7y + 7z = 0

x + y + z = 0

Therefore, equation of plane is