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Finding the angle between 2 vectors

  1. May 17, 2004 #1
    Could someone refresh my memory how to find the angle between 2 vectors in 3d, say:

    a= 4i + j + 2k
    b= -i +2j + k

    Thanks!
     
  2. jcsd
  3. May 17, 2004 #2

    enigma

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    dot product

    a.b = |a||b|cos (ang)
     
  4. May 17, 2004 #3
    So how would I find the angle for the two I posted?
     
  5. May 17, 2004 #4
    He just told you. Solve for theta and plug and chug.

    [tex]\theta = \arccos{\left( \frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|\right)}[/tex]

    [tex]\vec{a}\cdot\vec{b} = a_1b_1 + a_2b_2 + a_3b_3[/tex]
    and
    [tex]|\vec{a}| = \sqrt{{a_1}^2 + {a_2}^2 + {a_3}^2}[/tex]

    if [itex]\vec{a} = <a_1,a_2,a_3>[/itex] and likewise for b.

    cookiemonster
     
    Last edited: May 17, 2004
  6. May 17, 2004 #5
    Nice thinking Cookieman...
     
  7. May 17, 2004 #6
    Thank you!
     
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