# Find parametric equation

• May 2nd 2013, 02:06 PM
icelated
Find parametric equation
I have an odd problem in the book where i have no solution to and i am not sure if i am doing it correctly.

Let L be the line given by $x = 3-t, y=2+t, z= -4 +2t$

L intersects the plane $3x-2y+z=1$ at the point $P=(3, 2, -4)$

Find parametric equations for the line through P which lies in the plane and is perpendicular to L

Attempt:

Direction Vector v = $<-1,1,2>$

Normal Vector n = $<3, -2, 1>$

$v \times n = <5, 7, -1>$

$X = P + vt$

Point: $P=(3, 2, -4)$
v = $<-1,1,2>$

putting it together

$(3, 2, -4) + <-1,1,2>t$

Parametric equation: $x = 3-t, y = 2+t , z = -4 +2t$

Somehow, i dont think this is correct?

Thank you
• May 2nd 2013, 02:22 PM
Plato
Re: Find parametric equation
Quote:

Originally Posted by icelated
I have an odd problem in the book where i have no solution to and i am not sure if i am doing it correctly.
Let L be the line given by $x = 3-t, y=2+t, z= -4 +2t$
L intersects the plane $3x-2y+z=1$ at the point $P=(3, 2, -4)$
Find parametric equations for the line through P which lies in the plane and is perpendicular to L
Attempt:
Direction Vector v = $<-1,1,2>$
Normal Vector n = $<3, -2, 1>$
$v \times n = <5, 7, -1>$
$X = P + vt$
Point: $P=(3, 2, -4)$
v = $<-1,1,2>$
putting it together
$(3, 2, -4) + <-1,1,2>t$
Parametric equation: $x = 3-t, y = 2+t , z = -4 +2t$
Somehow, i dont think this is correct?

You have a mistake in concept. Your line is
$\\x=3+5t\\y=2+7t\\z=-4-t$

WHY?
• May 2nd 2013, 02:49 PM
icelated
Re: Find parametric equation
Are you saying i should use
$x = P + (v \times n) t$

$X = P + vt$
• May 2nd 2013, 02:55 PM
Plato
Re: Find parametric equation
Quote:

Originally Posted by icelated
I dont know what you mean. What you are trying to get.Are you saying i should use v X n instead of v?

You posted: Parametric equation: $\color{red}x = 3-t, y = 2+t , z = -4 +2t$
THIS IS CORRECT: Parametric equation: $x = 3+5t,~ y = 2+7t ,~ z = -4 -t$.