# Problem of the week #59 - May 13th, 2013

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#### Jameson

Staff member
The line $L_1$ goes through the point $(4,3,-2)$ and is parallel to the line defined by $(x=1+3t, y=2-4t, z= 3-t)$. If the point $(m,n,-5)$ is also on $L_1$ then find the values of $m$ and $n$.
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#### Jameson

Staff member
Congratulations to the following members for their correct solutions:

1) MarkFL
2) anemone
3) Sudharaka

Solution (from Sudharaka):
The line $$L_1$$ should go through the point $$(4,\,3,\,-2)$$ and should be parallel to the vector $$(3,\,-4,\,-1)$$. The equation of the line $$L_1$$ in vector form can be written as,

$L_1:\, (x,\,y,\,z)=(4,\,3,\,-2)+t(3,\,-4,\,-1)$

Since $$(m,\,n,\,-5)$$ is on $$L_1$$ we have,

$L_1:\, (m,\,n,\,-5)=(4,\,3,\,-2)+t(3,\,-4,\,-1)$

$\Rightarrow t=3$

$\therefore m=4+3t=13\mbox{ and }n=3-4t=-9$

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