1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Orthogonal vector condition

  1. May 2, 2016 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations
    u⋅v = |u||v| cos θ

    3. The attempt at a solution

    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
     
  2. jcsd
  3. May 2, 2016 #2

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
  4. May 2, 2016 #3
    Okay.. Just by inspection.. I get D as the answer..
    I thought too far and too much hahahaha...
    Thank you :smile:
     
  5. May 2, 2016 #4
    Anyway, can you show me the error in my calculation before?
    I'm curious where I get wrong
     
  6. May 2, 2016 #5

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    In both
    and
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Orthogonal vector condition
  1. Orthogonal vector (Replies: 7)

Loading...