Parametric Equations: Find Line P Passing Through P

[yazz912]

1. The problem statement, all variables and given/known

Find the equation of a line passing through the point P=(-1,2,3) that is parallel to the line of intersection of the planes 3x-2y+z=4 and x+2y+3z=5 . Express your answer in parametric equations .

2. Homework Equations

Cross product of normal vectors
N1 X N2

3. The Attempt at a Solution
Normally all other problems we've had to use cross product of the normals vectors of planes.
n1= <3,-2,1>
n2= <1,2,3>

Cross product I get < -8,-8,8>

Idk what my next step is since I am trying to find a line passing through point P PARALLEL to line of intersection?

 

[jackarms]

The vector you get from the cross product gives you your direction vector for the line -- it points in the direction of the line. Two lines are parallel if they have the same direction vectors (or really if their direction vectors are parallel). To find your line, assign it the vector of <-8, -8, 8> (or <-1, -1, 1> if you want to reduce it)

 

[LCKurtz]

1. The problem statement, all variables and given/known

Find the equation of a line passing through the point P=(-1,2,3) that is parallel to the line of intersection of the planes 3x-2y+z=4 and x+2y+3z=5 . Express your answer in parametric equations .




2. Homework Equations

Cross product of normal vectors
N1 X N2




3. The Attempt at a Solution
Normally all other problems we've had to use cross product of the normals vectors of planes.
n1= <3,-2,1>
n2= <1,2,3>

Cross product I get < -8,-8,8>

Idk what my next step is since I am trying to find a line passing through point P PARALLEL to line of intersection?

Can't you use your cross product vector for a direction vector for your line?

 

[tiny-tim]

hi yazz912!

Cross product I get < -8,-8,8>

looks fine so far

ok, you're only interested in the direction, so you may as well call that < -1,-1,1>, or even slightly better still < 1,1,-1> …

so what is the parametric equation of the line through P parallel to <1,1,-1> ?

 

[yazz912]

So using my point P=(-1,2,3)
And my direction vector of <-1,-1,1>

Would my parametric equation be

x= -1t -1
y= -1t +2
z= 1t +3

 

[tiny-tim]

yup!

 

[yazz912]

Ok thanks!:)