Two coplanar lines and finding the equation

[gundamshadow]

Homework Statement

Two coplanar lines, a and b are perpendicular to each other. a passes through the points (3,2,3) and (8,10,6). Find the equation for b if it passes through the point (7,49,25).

Homework Equations

The equation were trying to find is r = [x,y,z] + s [x1,y1,z1] + t [x2,y2,z2]

The Attempt at a Solution

Basically since the coordinates are perpendicular I used the cross product to find one direction vector. For my position vector I used (3,2,3). Now I'm not sure what to do with the last point (7,49,25) or what to do to find my second direction vector. I'm not even sure if I did the first part right. Help would be appreciated thanks!

EDIT: I originally posted this in a different section but somebody told me it'd be better if I post it here. So if a mod could remove the other thread in the physics section that'd be awesome.

 

[tiny-tim]

welcome to pf!

hi gundamshadow! welcome to pf!

have you drawn this?

you have three known points, B C and D, and you want the line through B perpendicular to CD

 

[gundamshadow]

Thank you for the welcome :)

So I'm assuming B is (3,2,3) and C is (8,10,6) etc.
In that case how would I go about finding direction vectors if they're perpendicular? Is it a combination of cross product of B and C?

EDIT: Also the term coplanar, does that mean the vectors in the equation have to be a multiple?

 

[tiny-tim]

come on!

it's a simple triangle question!

(you can use parallel lines, and cross products )

(coplanar means in the same plane … any vector in it will be a linear sum of any two distinct vectors in it)

 

[gundamshadow]

I`m sorry I am really lost now. I subtracted (3,2,3) and (8,10,6) and got (5,8,3). So that is my position vector I hope.

So as it stands the equation is r= (5,8,3) + s (xyz) + t (xyz)

How do I get the other coordinates for vector s and t

 

[tiny-tim]

hi gundamshadow!

I subtracted (3,2,3) and (8,10,6) and got (5,8,3).

yes, that's the direction of your line CD

so what is the line through B parallel to that?

 

[gundamshadow]

hi gundamshadow!


yes, that's the direction of your line CD

so what is the line through B parallel to that?

I thought that was the position vectorÉ And if its parallel does that mean that CD dot product by (7,49,25) will be zeroÉ

 

[tiny-tim]

I thought that was the position vectorÉ And if its parallel does that mean that CD dot product by (7,49,25) will be zeroÉ

you've lost me

what is the line through B parallel to CD?​

 

[gundamshadow]

Im kinda lost too. And I got (0,-3,8)

 

[gundamshadow]

EDIT: Realised bumping not allowed. Please delete post. Sorry!