How do you give parametric equations for the line through that is perpendicular to the plane (

seupeljewj

seupeljewj

Answered question

2022-06-16

How do you give parametric equations for the line through that is perpendicular to the plane ( 1 ,   3 ,   5 ) perpendicular to the plane 2 x - 3 y + 4 z = 11 ?

Answer & Explanation

Xzavier Shelton

Xzavier Shelton

Beginner2022-06-17Added 26 answers

Step 1
The plane
Π 2 x - 3 y + 4 z = 11 can be represented as
v , p - p 0 = 0
where
v = ( 2 , - 3 , 4 )
p = ( x , y , z )
p 0 = ( 0 , 0 , 11 4 )
Here, v is the normal to all the points p Π
Given now p 1 = ( 1 , 3 , - 5 ) the line passing by p 1 and orthogonal to Π is by construction
L p = p 1 + λ v where λ .
So L has as parametric equations:
{ x = 1 + 2 λ y = 3 - 3 λ z = - 5 + 4 λ

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