# Vectors problem

1. Feb 23, 2007

### vinay_mamgain

i have just joined ur sit e
can u help me out
if we have the initial point of two vectors and equations of these vectors , how can we find the intersection point of these vectors

2. Feb 23, 2007

### HallsofIvy

Staff Emeritus
?? Vectors are "free floating"- only specific representations have initial points. And even those may not intersect- they may not reach far enough.
If you mean you have two lines, one passing through $(x_0,y_0,z_0)$ in the same direction as vector Ai+ Bj+ Ck, the other passing through $(x_1, y_1, z_1)$, in the same direction as vector Ui+ Vj+ Wk, then the first line can be written in parametric equations $x= x_0+ At$, $y= y_0+ Bt$, $z= z_0+ Ct$ and the second line can be written in parametric equations $x= x_1+ Ut$, $y= y_1+ Vt$, $z= z_1+ Wt$. Set "x=x", "y= y", "z= z", and solve the resulting three equations for s and t.
Of course, in general, three equations won't give just two unknown values- in three dimensions most lines are "skew" and don't intersect. If you are working in 2-dimensions, (x, y), just ignore the z equations and you have two equations to solve for s and t.

3. Feb 24, 2007

### vinay_mamgain

u got me right.

here is one other problem.
given initial points of two vector with their equation
what will be the minimum distance between them if they dont intersect.

i had read one of the answer written in ur site , that subtract one vector from the other and taking the magnitude of that resultant vector will give us result.

now suppose if our one vector start at (1,0,0) with equation 2i +0j + 0k i.e 2i. Other has (2,0,0) as initial point with eq 2i( as i think two parallel vectors with equal magnitude have same equation).then according to above solution ,the answer is zero. pease if possible give formula.

thanks
vinay