Hello im currently studding math in High school / college level,
And today we had to calculate if 2 3d-vectors would cross each other, and since i diddent like to go though the 5-6 steps the book taugth us, i came up with a formular that could handle most of the steps in 1 take.
The goal is to calculate S (and T) so you can calculate the point of collision if any exist.
I get two 3d-vectors as following: "i.stack.imgur.com/XmFEn.png"
Where L = Lenght of the vector, and O = Oriantation of the vector.
These numbers can all be positive, negative and zero.
- on the picture shows the real math questions data.
I guess no more detail is required since the question is about how to shorten (if you can) a formular of this type and not how to get to this formular.
The most basic way to show the formular would be this:
Are there anyway to remove both of the X'es, Or in anyway shorten the formular?
The real formula is this one:
where the last is the current state of the formula.
No, not really. You can multiply by $x/x=1$, to get an expression without fractions within fractions:
$$\frac{b-\frac{a}{x}}{d+\frac{c}{x}}=\frac{bx-a}{dx+c},$$
but no further simplification can be achieved (without any further information about the parameters at least).