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Unit vector problem

  1. Sep 29, 2015 #1
    1. The problem statement, all variables and given/known data
    if a =3i-4j
    find a unit vector perpendicular a

    2. Relevant equations

    3. The attempt at a solution
    <a> = <3 , -4>
    <n> = <x, y> : x² + y² = 1
    <a>•<n> = 3x-4y = 0

    y = (3/4)x
    x² + (9/16)x² = 1
    25x² = 16
    x = -4/5, 4/5
    y = -3/5, 3/5

    There are two unit vectors normal to a which have opposite directions:
    n =(4i + 3j)/5
    n = -(4i+3j)/5

    This is the answer that given by my textbook. Can somebody explain to me the 2nd step <n> = <x, y> : x² + y² = 1
    I do not understand why it use x^2+y^2=1 as this is circle equation.
  2. jcsd
  3. Sep 29, 2015 #2


    Staff: Mentor

    Its saying to define a vector n with components x,y such that x^2 + y^2 =1 in other words that n is a unit vector with components x and y.

    Dotting it with the known vector gives you the other equation so that you now have two equations in x and y and thus can solve for x and y
  4. Sep 29, 2015 #3


    User Avatar
    Science Advisor

    Yes, it is a circle centered at the origin with radius 1. So any unit vector with "tail" at the origin has its "tip" on that circle. Any unit vector <x, y> satisfies x² + y² = 1.
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