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Homework Help: Unit Vectors

  1. Nov 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Given a=2i+3j+k, b=i+2j+k, c=-i-j+k, calculate;

    a)unit vectors b^ and c^ in the directions of b and c respectively.
    b)the angle between a and c

    2. Relevant equations

    3. The attempt at a solution
    I don't understand a) at all,
    but b is just a simple dot product question.

    Any ideas for a) ?
  2. jcsd
  3. Nov 16, 2008 #2


    User Avatar
    Homework Helper

    Do you know what a unit vector is?
  4. Nov 16, 2008 #3


    Staff: Mentor

    a) For any vector x other than the zero vector 0i + 0j + 0k, the vector 1/|x| * x will be a unit vector with the same direction as x.

    b) You didn't ask, but one definition of the dot product of vectors a and b is [tex]a \cdot b = |a||b]| cos \theta[/tex]
    where [tex]\theta[/tex] is the angle between the two vectors.
  5. Nov 16, 2008 #4
    Thank you both. Tbh, I'm still not entirely sure what a unit vector is though, but I do understand Mark44's formula for calculating. Ta
  6. Nov 16, 2008 #5


    Staff: Mentor

    A unit vector has a magnitude (or length) of 1 unit. You can normalize any nonzero vector by shrinking it or lengthening it to a vector with the same direction, and magnitude 1.
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