Given : Equations of lines –

Line 1 : or

Line 2 : or

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 = 5 , y₁ = 7 , z₁ = -3 , a₁ = 4 , b₁ = 4 , c₁ = -5

x₂ = 8 , y₂ = 4 , z₂ = 5 , a₂ = 7 , b₂ = 1 , c₂ = 3

Now,

= 51 + 141 – 192

= 0

Hence, given two lines are coplanar.

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

17x – 85 – 47y + 329 – 24z – 72 = 0

17x - 47y – 24z + 172 = 0

Therefore, equation of plane is

17x - 47y – 24z + 172 = 0