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!

Homework Help: Dot product proof

  1. Apr 27, 2010 #1
    If X is an N vector, is it 1) possible for X*X to be negative? 2) if x*x=0, what is X.

    I am having trouble writing the proper proof. for 1 I stated that it is impossible for X*X to be negative bc if x is positive, X*X is positive and if x is negative, -X*-X is still positive.

    for 2 I stated the properties of multiplication; in order for a product to = 0 one of the components must be 0.

    Can someone advise on the proper method for writing these proofs?

    Thanks
     
  2. jcsd
  3. Apr 27, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    What is X.X in terms of the components of X?
     
  4. Apr 28, 2010 #3
    Not sure what youare asking, but X*X is the dot product of X. X is an arbitrary vector.
     
  5. Apr 28, 2010 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    X is a vector, it has components. I.e. X=(x1,x2,...,xn). What's X.X in terms of the components, the little x's?
     
  6. Apr 28, 2010 #5

    lanedance

    User Avatar
    Homework Helper

    I think Dick is asking you to examine how the dot product is caclulated in terms of the components of the vector.

    Say X = (x1, x2, .. ,xn)^T

    How do you calculate the dot product X*X in terms of the xi's?
     
  7. Apr 28, 2010 #6
    X= ( X1, X2, X3)
    the dot product should be X1^2+X2^2 +X3^2. Squares cant be negative.


    if X1^2+X2^2 +X3^2 =0 then X1 X2 and X3 must be zero

    Is this all there is to it?
     
  8. Apr 28, 2010 #7

    lanedance

    User Avatar
    Homework Helper

    looks good to me
     
  9. Apr 28, 2010 #8

    lanedance

    User Avatar
    Homework Helper

    though you should generalise it to the n dimensional case rather than just 3
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook