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Dot product?

  1. Jun 10, 2017 #1
    1. The problem statement, all variables and given/known data
    Im given vectors:

    b = x hat + y hat
    c = x hat + z hat

    2. Relevant equations
    http://imgur.com/a/iHTOT

    3. The attempt at a solution
    so I have 2 eq's... one says:
    r * s = rscos(theta)

    the other is a summation saying multiply x component 1 with x component 2, add y component 1 with y component 2, and so on.

    Ok so I start with method 2: 1*1 x hat + 1* 0 y hat + 0*1 z hat

    so you end with 1 (my books answer).

    But when I use "r * s = rscos(theta)" I find the angle between them is 90 degrees so I get 0.

    Whv does 1 formula work in this case but the other doesnt
     
  2. jcsd
  3. Jun 10, 2017 #2

    Mark44

    Staff: Mentor

    No, this isn't what it is saying. What you get from a dot product is a number -- no vectors involved.

    There are two forms for the dot product of vectors in ##\mathbb{R}^3##: one that involves the cosine of the angle between the vectors, and the other that involves the sum of the products of the components.

    Assuming these are your vectors. ##\vec r = <1, 1, 0>## and ##\vec s = <1, 0, 1>##, then ##\vec r \cdot \vec s = 1 \cdot 1 + 1 \cdot 0 + 0 \cdot 1 = 1##

    Both formulas work, but the angle between the two vectors is not 90° - they are actually 60° apart.
     
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