# Vectors problem

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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

HallsofIvy
Homework Helper
?? 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.