Work out the line equation (parametric equation)

[Hernaner28]

Homework Statement

Let the point A and v1,v2,v3 non-coplanar vectors.
Let the plane
$${\pi _1})P=A+{\lambda _1}{v_1}+{\lambda _2}{v_2}$$

Consider any vector u non-colinear with v3 and the plane:
$${\pi _2})P=A+{\lambda _3}{v_3}+{\lambda _4}u$$

2. Task
Work out the equation of the line
$$r={\pi _1}\cap {\pi _2}$$

The Attempt at a Solution

No idea how to start. I just know that the point A belongs to both planes and the point A belongs to a line with the equation form of: $$A+\lambda v$$ but I don't know what to do next.

Thanks!

 

[SammyS]

Homework Statement

Let the point A and v1,v2,v3 non-coplanar vectors.
Let the plane
$${\pi _1})P=A+{\lambda _1}{v_1}+{\lambda _2}{v_2}$$

Consider any vector u non-colinear with v3 and the plane:
$${\pi _2})P=A+{\lambda _3}{v_3}+{\lambda _4}u$$

2. Task
Work out the equation of the line
$$r={\pi _1}\cap {\pi _2}$$

The Attempt at a Solution

No idea how to start. I just know that the point A belongs to both planes and the point A belongs to a line with the equation form of: $$A+\lambda v$$ but I don't know what to do next.

Thanks!

Find a vector, n₁, normal to plane π₁, and a vector, n₂, normal to plane π₂.

How is the line of intersection of the two planes oriented w.r.t. these two normal vectors, n₁ and n₂ ?