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I am new to analytical geometry and excuse me for my notations. We have four lines:

$l_1: u_1x + v_1y + r_1 = 0$

$l_2: u_2x + v_2y + r_2 = 0$

$m_1: u_3x + v_3y + r_3 = 0$

$m_2: u_4x + v_4y + r_4 = 0$

We know that $l_1$ and $l_2$ cross int $(l_1, l_2)$ and $m_1$ and $m_2$ cross in $(m_1, m_2)$

Find the straight line $p$ which is equal to $p = (l_1, l_2)(m_1, m_2)$.

from $(l_1, l_2 ) \Rightarrow u_1x + v_1y + r_1 + u_2x + v_2y + r-2 = 0$

from $(r_1, r_2 ) \Rightarrow u_3x + v_3y + r_3 + u_4x + v_4y + r_4 = 0$

right?

if so I don't understand what the notation in $p = (l_1, l_2)(m_1, m_2 )$, really means, actually I don't quite undestand the idea that $(l_1, l_2 ) \Rightarrow l_1 + l_2 = 0$

StubbornAtom
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murloc
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1 Answers1

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If $(l_1, l_2)$ is for the intersection $I$ of $l_1$ and $l_2$;

If $(m_1, m_2)$ is for the intersection $J$ of $m_1$ and $m_2$;

Notation $p = (l_1, l_2)(m_1, m_2 )$ which is is not classical, should mean the straight line $IJ$...

I dont follow you when you write $l_1+l_2=0$. (The "right ?" appeals answer "no!")

What you have to do is

1) solve the linear system of 2 equations formed by $l_1$ and $l_2$ to obtain the coordinates of $I$, then

2) do the same for $J$, then

3) compute the equation of straight line $IJ$.

Jean Marie
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