Finding velocity along a vector, given velocity in xyz

[Bucky]

Homework Statement

I am attempting to program a simulation of a ball hitting a wall (breakout, basically), and am having problem with the maths elements. I have the angle at which the object strikes the wall, and currently I am working on the separation velocity. However, I don't know how to find this.

I have the velocity of the ball in the XYZ, but don't know how to combine these into a velocity along a vector. Also how would i then take the velocity after impact and separate this back into the XYZ components? I think it would involve scaling the values but I'm not certain on this.

Homework Equations

v^2 = u^2(cos^2 a + e^2 * sin^2 a)
(I have a and e, and need u to solve the equation)

The Attempt at a Solution

Well...everything up till here. Using a plane->vector intersection formula (n.b = |n||b|sinA ...where n is the plane normal, b is the vector and A is the angle) to find the angle the vector makes with the plane.

 

[weatherhead]

bear in mind that N.E.L (Newton's experimental law) affects only the component of velocity perpendicular to the plane, so probably your "xyz" velocities are what you need to work out components of velocity after the collision. I think your relevant equation is the result from taking this into account...

Combining components of velocity into a vector, by which I assume you mean direction and magnitude, just convert the vector in three components into a polar form. However, that's probably not so useful to you working in three dimensions as you'd need spherical polars or cylinder polars... Anyway, to get the magnitude just do pythag on the components. r = sqrt(x_component^2+y_component^2+z_component^2)

Converting the vector "back" into components is just the opposite problem, essentially converting a polar coordinate into cartesian coordinates. Do you have access to a computer or calculator to solve this problem?