How do you find parametric equations for the line of intersection of the planes 2x + 5z + 3 = 0 and x -3y + z + 2 = 0?

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Answer 1 · 2017-03-20T15:41:55

See below.

Given the planes

$Pi_1->2x+5z+3=0$
$Pi_2->x-3y+z+2=0$

The line

$L=Pi_1 nn Pi_2$ is the solution of the system

$((2,0),(1,-3))((x),(y))=((-3),(-(z+2)))$

Solving for $x,y$ we have

${(x=-3/2-5/2 lambda),(y=1/6-lambda/2):}$

now substituting into any of $Pi_1,Pi_2$

$2(-3/2-5/2 lambda)+5z+3=0$ obtaining

$z=lambda$ and finally

$L->{(x=-3/2-5/2 lambda),(y=1/6-lambda/2),(z=lambda):}$