Question

The lines l and m have vector equations

r=i+j+k+s(i−j+2k) and r=4i+6j+k+t(2i+2j+k)

respectively. (i) Show that l and m intersect.

Answer 1

Show they intersect by finding s and t that make them equal
\[\left(\begin{matrix}1 \\ 1\\1\end{matrix}\right)+s\left(\begin{matrix}1 \\ -1\\2\end{matrix}\right)=\left(\begin{matrix}4 \\ 6\\1\end{matrix}\right)+t\left(\begin{matrix}2 \\ 2\\1\end{matrix}\right)\]

Answer 2

rewrite this as
\[s\left(\begin{matrix}1 \\ -1\\2\end{matrix}\right)+t \left(\begin{matrix}-2 \\ -2\\-1\end{matrix}\right)=\left(\begin{matrix}3 \\ 5\\0\end{matrix}\right)\]

Answer 3

Thanks :D

Answer 4

I got it from here :D

Answer 5

which can be viewed as the augmented matrix problem
\[\left[\begin{matrix}1 & -2 & 3\\-1 & -2 & 5 \\ 2 &-1&0\end{matrix}\right]\]