What is the equation of the planes containing two lines???

Let take two lines:
Let the equations of the line be :
x-2/2 = y +4/3 = 2-z/5

And x = 3 + 4t
y = -4 + 6t
z = 5-10t

So the first equation can be written as
x = 2 + 2t
y = -4 + 3t
z = 2-5t

So the lines have direction ratios as v1 ( 4,6,-10) and v2( 2,3,-5)
Putting t = 0, we get points on the lines as p1( 3,-4,5) and p2(2,-4,2)
Constructing a vector v3 = p1 - p2 = ( 1,0 ,3)

Now for normal take cross product of n=  v3 x ( v1 or v2)
So equation of plane is n.( r - p1) = 0, put the value and get the equation of the plane.


 

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