• Support PF! Buy your school textbooks, materials and every day products Here!

Orthogonal projection onto a plane spanned by two vectors

  • #1

Homework Statement


x = <0, 10, 0>
v1 = <4, 3, 0>
v2 = <0, 0, 1>

Project x onto plane spanned by v1 and v2

Homework Equations


Projection equation

The Attempt at a Solution


I took the cross product
k = v1xv2 = <3, -4, 0>

I projected x onto v1xv2
[(x*k)/(k*k)]*k = <-4.8, 6.4, 0 = p

I finished by
x - p = <4.8,3.6,0>

Is this correct?
 

Answers and Replies

  • #2
andrewkirk
Science Advisor
Homework Helper
Insights Author
Gold Member
3,792
1,390
You can check this as follows:

Step 1: check that (x-p) is in the plane, ie check that it can be expressed as a linear combination of v1 and v2.
Step 2: check that (x-p) is perpendicular to p (take the dot product)
Step 3: check that (x-p) + p = p

If these are all correct then the solution is correct.
 

Related Threads for: Orthogonal projection onto a plane spanned by two vectors

Replies
1
Views
1K
Replies
6
Views
1K
  • Last Post
Replies
2
Views
3K
Replies
3
Views
2K
Replies
3
Views
878
Replies
5
Views
10K
  • Last Post
Replies
1
Views
3K
Top