Q. 54.0( 1 Vote )

Prove that the li

Answer :

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 = 2 , y1 = 4 , z1 = 6 , a1 = 1 , b1 = 4 , c1 = 7


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


Now,






= 21 - 98 + 77


= 0



Hence, given two lines are coplanar.


Equation of plane passing through line 1 and line 2 is given by,






-7x + 14 + 14y - 56 – 7z + 42 = 0


- 7x + 14y – 7z = 0


x – 2y + z = 0


Therefore, equation of plane is


x – 2y + z = 0


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