- #1
sachi
- 63
- 1
we have r = a + ut, r = b + vt, where a,u,b,t are all vectors and t is the variable for time. We need to show that the collision time is
a.(b X u)/v.(b X u) where . is the dot product and X is the cross product.
this is quite straightforward. we then need to find the time if a,b,u,v are coplanar. This means that v.(b X u) = 0, which is not allowed in our expression for the time as the denominator would go to zero. I can derive a different expression for the time using the scalar product,
t=(a-b).a/(v-u).a
but I have a feeling this may be equivalent. I can't see why this eq'n would only apply when the vectors were coplanar.
The question does not specify that a does not equal b and that u does not equal v. It might be that the two lines are skew and the collision never takes place (i.e time is infinite).
Thanks
a.(b X u)/v.(b X u) where . is the dot product and X is the cross product.
this is quite straightforward. we then need to find the time if a,b,u,v are coplanar. This means that v.(b X u) = 0, which is not allowed in our expression for the time as the denominator would go to zero. I can derive a different expression for the time using the scalar product,
t=(a-b).a/(v-u).a
but I have a feeling this may be equivalent. I can't see why this eq'n would only apply when the vectors were coplanar.
The question does not specify that a does not equal b and that u does not equal v. It might be that the two lines are skew and the collision never takes place (i.e time is infinite).
Thanks