closed

lj789

12

closed

(edited 13 years ago)

Reply 1

ghostwalker

17

Original post by lj789

Topic: Vector

prove if 2 straight lines, r = a + ku, r = b + hv intersect, then v*(b X u) = v*(a X u)

b X u is a cross product
* means dot product

any help is appreciated thanks

Since you know the two lines meet the obvious thing is to specify their point of intersection in terms of the two lines and equate.

Then perform the appropriate vector and dot multiplications to get into the desired form. Note that some terms will evaluate as zero.

Have a go, and post your working if you're still stuck.

Reply 2

lj789

OP

12

Original post by ghostwalker

Since you know the two lines meet the obvious thing is to specify their point of intersection in terms of the two lines and equate.

Then perform the appropriate vector and dot multiplications to get into the desired form. Note that some terms will evaluate as zero.

Have a go, and post your working if you're still stuck.

del-

(edited 13 years ago)

Reply 3

DFranklin

18

If they intersect, then you know that there are values for h and k such that the two vectors are the same.

That is, you know that a+ku = b+hv (even though you don't know what h and k are).