Orthogonal vector condition

  • Thread starter terryds
  • Start date
  • #1
392
13

Homework Statement



Vector u, v, and x are not zero. Vector u + v will be perpendicular (orthogonal) to u-x if

A. |u+v| = |u-v|
B. |v| = |x|
C. u ⋅ u = v ⋅ v, v = -x
D. u ⋅ u = v ⋅ v, v = x
E. u ⋅ u = v ⋅ v

Homework Equations


u⋅v = |u||v| cos θ

The Attempt at a Solution


[/B]
Two vectors are orthogonal to each other if the dot product is zero.

(u + v) ⋅ (u - x) = 0
(u ⋅ u) - (u ⋅ x) + (v ⋅ u) - (v ⋅ x) = 0
u ⋅ (u + v) - x ⋅ (u + v) = 0
u ⋅ (u + v) = x ⋅ (u + v)

u = x

or

u ⋅ (u - x) + v ⋅ ( u - x) = 0
u ⋅ (u - x) = - v (u - x)

so, u = -v

x = -v
v = -x

It seems the answer is C
But, how to get the condition u⋅u = v⋅v
Thanks in advance
 

Answers and Replies

  • #2
blue_leaf77
Science Advisor
Homework Helper
2,629
784
It seems the answer is C
I don't think so.
Just do it by inspection on the equation (u ⋅ u) - (u ⋅ x) + (v ⋅ u) - (v ⋅ x) = 0. Try the answer choices one by one to find which one satisfies that equation.
 
  • #3
392
13
I don't think so.
Just do it by inspection on the equation (u ⋅ u) - (u ⋅ x) + (v ⋅ u) - (v ⋅ x) = 0. Try the answer choices one by one to find which one satisfies that equation.
Okay.. Just by inspection.. I get D as the answer..
I thought too far and too much hahahaha...
Thank you :smile:
 
  • #4
392
13
I don't think so.
Just do it by inspection on the equation (u ⋅ u) - (u ⋅ x) + (v ⋅ u) - (v ⋅ x) = 0. Try the answer choices one by one to find which one satisfies that equation.
Anyway, can you show me the error in my calculation before?
I'm curious where I get wrong
 
  • #5
blue_leaf77
Science Advisor
Homework Helper
2,629
784
In both
u ⋅ (u + v) = x ⋅ (u + v)
and
u ⋅ (u - x) = - v (u - x)
you are concluding that if ##(a,b) = (c,b)## for some vector(s) ##b##, then ##a=c## - this conclusion is incorrect. It would have been true had the vector ##b## stands for any vectors in the space.
 
  • Like
Likes terryds

Related Threads on Orthogonal vector condition

  • Last Post
Replies
7
Views
5K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
17
Views
3K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
12
Views
2K
Replies
2
Views
1K
  • Last Post
Replies
9
Views
686
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
4
Views
3K
Top