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**Fratricide** A spider builds a web in a garden. The position vectors of the ends *A* and*B* relative to an origin *O* of a strand of the web are given by *OA* = 2**i** + 3**j** + **k** and *OB* = 3**i** + 4**j** + 2**k**. Another web strand *MN* has end points *M* and *N* with position vectors *OM = 4***i** + 2**j** - **k** and *ON* = 6**i** + 10**j** + 9**k**. The spider decides to continue *AB* to join *MN*. Find the position vector of the point of contact.

I worked out *AB* to be **i** + **j** + **k**, but I don't know where to go from there. We've just started vectors so most of this is new to me.

Thanks.