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
explanation: The document is a forum thread where a user asks how to find the angle between two vectors in 3D space. Another user provides the formula for the dot product and the method to find the angle. The original poster then asks for clarification, and a third user provides a more detailed explanation with the specific formula and steps to solve the problem.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: 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
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a forum thread where a user asks how to find the angle between two vectors in 3D space. Another user provides the formula for the dot product and the method to find the angle. The original poster then asks for clarification, and a third user provides a more detailed explanation with the specific formula and steps to solve the problem.
  
  Label: question-and-answer