Answer :

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


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