Convert from plane equation to scalar equation

  • #1
DespicableMe
41
0

Homework Statement



When we're given an equation in form r = r0 + sa + tb, how do we convert it to scalar form Ax + By + Cz + D = 0?

I've been having trouble with plane form, but I can do it fine when its given in 2- or 3-D form.
 

Answers and Replies

  • #2
36,429
8,409

Homework Statement



When we're given an equation in form r = r0 + sa + tb, how do we convert it to scalar form Ax + By + Cz + D = 0?

I've been having trouble with plane form, but I can do it fine when its given in 2- or 3-D form.

In your vector equation, r = r0 + sa + tb, the vectors a and b are in the plane, so their cross product, a X b, would be perpendicular to the plane.

The vector r0 is a vector from the origin to a point on the plane.

Once you have a normal to the plane and a point on it, the equation of the plane is N [itex]\cdot[/itex](x - P) = 0, where N is your normal, x = <x, y, z>, and P is the point you know.
 

Suggested for: Convert from plane equation to scalar equation

Replies
1
Views
411
Replies
6
Views
296
Replies
2
Views
487
Replies
25
Views
307
Replies
1
Views
212
Replies
12
Views
672
  • Last Post
Replies
32
Views
714
Replies
3
Views
261
Replies
2
Views
228
Replies
42
Views
1K
Top