text: Finding the angle between 2 vectors
  
  1. May 17, 2004
  
  PinkFlamingo
  
  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. May 17, 2004
  
  enigma
  
  Staff Emeritus
  dot product
  
  a.b = |a||b|cos (ang)
  
  3. May 17, 2004
  
  PinkFlamingo
  
  So how would I find the angle for the two I posted?
  
  4. May 17, 2004
  
  He just told you. Solve for theta and plug and chug.
  
  $$\theta = \arccos{\left( \frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|\right)}$$
  
  $$\vec{a}\cdot\vec{b} = a_1b_1 + a_2b_2 + a_3b_3$$
  and
  $$|\vec{a}| = \sqrt{{a_1}^2 + {a_2}^2 + {a_3}^2}$$
  
  if $\vec{a} = <a_1,a_2,a_3>$ and likewise for b.
  
  Last edited: May 17, 2004
  5. May 17, 2004