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Couple of Calc III questions - Vectors, Continuity

  1. Jan 30, 2012 #1
    1. The problem statement, all variables and given/known data

    Hey guys, I have two separate questions.

    1.)

    I am asked for a unit vector pointing from P = (1,2) to Q = (4,6)

    In physics, every vector I've ever worked with started at the origin, so these feel weird.

    I initially thought that it would simply be 3i + 4j, the differences of each coordinate. However, my book gives the answer as (3/5)i + (4/5)j, they divided each number by sqrt(3^2 + 4^2). But why? Why specifically divide by that? If I understand correctly, if you divide both numbers by any one number, the vector will still point the same way because you just make a similar triangle. Why divide by vector length?

    2.)

    Limits and Continuity has been very confusing for me.

    I am asked to show that f(x,y) does not have a limit as (x,y) -> (0,0), and it says (Hint: use the line y = mx)

    The function is (x^2 - y^2)/(x^2 + y^2). How do I use y = mx?

    2. Relevant equations



    3. The attempt at a solution

    Looking for more of a explanation to help me better understand, not a solution.
     
  2. jcsd
  3. Jan 30, 2012 #2

    Dick

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    Homework Helper

    1) you divide by the length because they asked for a 'unit vector'. 3i+4j points in the right direction but it doesn't have length 1. 3i/5+4j/5 does. 2) Just put y=mx into the function you are trying to find the limit of and simplify.
     
  4. Jan 30, 2012 #3
    Thank you!
     
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