# Thread: Finding the Parametic equation

1. ## Finding the Parametic equation

Hi

Can someone tell me how to do the following question:
Find the parametric equation of the straight line of intersection of the planes:
$-2x+11y+4z=-1$
$-x+2y+z=3$

P.S

2. Originally Posted by Paymemoney
Hi

Can someone tell me how to do the following question:
Find the parametric equation of the straight line of intersection of the planes:
$-2x+11y+4z=-1$
$-x+2y+z=3$

P.S

This question is not advanced algebra but analytic geometry.

1) Solve the system of two equations determined by the planes' eq's to find the intersection of the two planes.

2) Now parametrize the line you found in (1).

Do the above and if you get stuck somewhere write back.

Tonio

3. the first part i tried to use Gaussian elimination to determine the intersection but i got $-x+\frac{11}{2}y-\frac{4}{7} = \frac{3}{2}$

so then how would i parametrize the equation i got.?

4. after doing it again i got

x=-1-t
y=12-11t
z=5-5t

5. Originally Posted by Paymemoney
after doing it again i got

x=-1-t
y=12-11t
z=5-5t

Input the above in the first eq. and you'll see it is completely wrong...

Multiply the 2nd. equation by -2 and add to this the 1st. one to obtain $7y+2z=-7\Longrightarrow y=-1-\frac{2}{7}z$ , and inputting

this in the 2nd. original eq. we get $-x-2-\frac{4}{7}z+z=3\Longrightarrow x=-5+\frac{3}{7}z$ , and thus the intersection line is given

by $\left\{\begin{pmatrix}-5+\frac{3}{7}t\\{}\\-1-\frac{2}{7}t\\{}\\t\end{pmatrix}\,,\,t\in\mathbb{R }\right\}$ .

The above is already a parametrization, but your teacher may want you to write it as $u+tv\,,\,u,v$ vectors

on the line, $t=$ the real parameter.

Tonio