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

Vector Analysis

  • Thread starter dpa
  • Start date
  • #1
dpa
147
0

Homework Statement



Let x,y is in Vn, such that x is not equal to zero.
Show that you can find vectors y and y// is in Vn such that y=y + y// and y// is parallel to x and y is perpendicular to x.

Homework Equations


x//y => x=ky
x.y=0 if x┴y

The Attempt at a Solution


I calculated the components of y along y and y// and showed that the synthesis of these gives y. I was adviced to use x as well. So I need different method.

By supposing y//=kx,
y=y-y//
we write,
kx.(y-y//)=0
and I was asked to find k and show,y=y + y//. I have no idea how to proceed after the above line.

Thank You
 

Answers and Replies

  • #2
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
180
Do you know how to project a vector onto another vector?
 
  • #3
dpa
147
0
I was suggested not to use vector projections that are in trigonometric forms.
As for the y||=(x.y/x^2).x form,
I know that what I can do is find
y||=(y.kx/(kx)^2).kx [sorry, k is not bold here]
and yperp.=y-xk.,
I have no idea hence forth.
 
  • #4
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,394
180
I was suggested not to use vector projections that are in trigonometric forms.
As for the y||=(x.y/x^2).x form,
.
This is what I meant by vector projection. In fact, you can take k = (x.y/x^2), can't you?
 

Related Threads on Vector Analysis

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
933
  • Last Post
Replies
20
Views
4K
  • Last Post
Replies
16
Views
862
  • Last Post
Replies
5
Views
421
Top