Question

What forms the intersection of two planes?

Answer 1

Answer: Two intersecting planes always form a line

Explanation:

Suppose the two planes are

ax + by + cz = d and ex + fy + gz = h

then the vector (a, b, c) is normal to the first plane and (e, f, g) is normal to the second plane. Hence the vector

(p, q, r) = (a, b, c) times (e, f, g),

the cross product of (a, b, c) and (e, f, g), is in the direction of the line of intersection of the line of intersection of the planes. Thus the line of intersection is

x = x₀ + p, y = y₀ + q, z = z₀ + r

where (x₀, y₀, z₀) is a point on both planes. You can find a point (x₀, y₀, z₀) in many ways. For example choose x = x₀ to be any convenient number, substitute this value into the equations of the planes and then solve the resulting equations for y and z.

ps i hope this helps

Answer 2

In case two planes cross each other, the crossing point will continuously be a line. where r r_0 r0​ may be a point on the line and v is the vector result of the cross item of the typical vectors of the two planes.

Explanation: