How do you find parametric equations for the line of intersection of the planes 2 x + 5

Jayla Christensen

Jayla Christensen

Answered question

2022-06-28

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

Answer & Explanation

Patricia Curry

Patricia Curry

Beginner2022-06-29Added 15 answers

Step 1
Given the planes
Π 1 2 x + 5 z + 3 = 0
Π 2 x - 3 y + z + 2 = 0
The line
L = Π 1 Π 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 λ y = 1 6 - λ 2
now substituting into any of Π 1 , Π 2
2 ( - 3 2 - 5 2 λ ) + 5 z + 3 = 0 obtaining
z = λ and finally
L { x = - 3 2 - 5 2 λ y = 1 6 - λ 2 z = λ

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