Determine whether r1 and r2 collide or intersect:
r1(t) = <t^2 + 3 , t + 1 , 6t^-1 >
r2(t) = <4t , 2t -2 , t^2 - 7>
I am completely lost in this problem and was hoping for a just a hint at where to begin. I'm unsure what it even means if two lines collide or intersect.
I've done a similar problem that read:
r1(t) = < 1 , 0 , 1 > + t<3, 3, 5 >
r2(t) = < 3, 6, 1 > +t<4, -2, 7>
I did it by multiplying the scalars out and adding the two vectors. Then setting the x components of the two lines equal to each other...same with y and z. This gives me three equations with which i use to solve for t1 and t2. Finally, plugging the t values into the third equation will prove whether or not the lines intersect if the equation is satisfied with the two t values.
I'm unsure what 'collision' is. Do i approach this problem the same way?