1. Vectors #1

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

2. Re: Vectors #1

Originally Posted by Fratricide
A spider builds a web in a garden. The position vectors of the ends A andB relative to an origin O of a strand of the web are given by OA = 2i + 3j + k and OB = 3i + 4j + 2k. Another web strand MN has end points M and N with position vectors OM = 4i + 2j - k and ON = 6i + 10j + 9k. 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.
$\vec{AB}=\vec{OB}-\vec{OA}$

$\vec{MN}=\vec{ON}-\vec{OM}$

$L_{AB}(t)=\vec{OB}+t\vec{AB}$

$L_{MN}(s)=\vec{OM}+s\vec{MN}$

solve for $L_{AB}(\hat{t})=L_{MN}(\hat{s})$

then the point of intersection is $L_{AB}(\hat{t})=L_{MN}(\hat{s})$