Find the vector and Cartesian forms of the equations of the plane containing the two lines and ..

Given : Equations of lines -

To Find : Equation of plane.

Formulae :

1) Cross Product :

If are two vectors

then,

2) Dot Product :

If are two vectors

then,

3) Equation of plane :

If two lines are coplanar then equation of the plane containing them is

Where,

Given equations of lines are

Let,

Where,

Now,

Therefore,

= 6 – 56 – 48

= - 98

………eq(1)

Equation of plane containing lines is

Now,

From eq(1)

Therefore, equation of required plane is

This vector equation of plane.

As

= 6x – 28y + 12z

Therefore, equation of plane is

6x – 28y + 12z = -98

6x – 28y + 12z + 98 = 0

This Cartesian equation of plane.