Vector manipulations and stuff

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SUMMARY

The discussion focuses on calculating the angle between the position vectors (3,-4,0) and (-2,1,0), which is determined to be 153.4° using both the dot product definition involving magnitudes and components. Additionally, the perpendicular vector is derived from the cross product of the two vectors, resulting in (0,0,-5) or (0,0,5). The direction cosines for the perpendicular vector are correctly calculated as 0, 0, and -1.

PREREQUISITES
  • Understanding of vector operations, specifically dot product and cross product.
  • Knowledge of calculating angles between vectors in three-dimensional space.
  • Familiarity with direction cosines and their calculation.
  • Basic proficiency in handling 3D coordinate systems.
NEXT STEPS
  • Study the properties and applications of the dot product in vector analysis.
  • Learn about the geometric interpretation of the cross product in three-dimensional space.
  • Explore the concept of direction cosines in greater detail, including their applications in physics.
  • Practice solving problems involving angles and perpendicular vectors in 3D geometry.
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Students studying vector mathematics, educators teaching geometry, and anyone interested in mastering three-dimensional vector operations.

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Homework Statement



Find the angle between the position vectors to the points (3,-4,0) and (-2,1,0) and find the direction cosines of a vector perpendicular to both.

Homework Equations



The Attempt at a Solution



You calculate the angle using the two definitions of the dot product (one that uses the magnitude of the vectors and the other that uses the components of the vectors). The answer is 153.4°. Is it right?

The perpendicular vector is the cross product of the two given vectors (the order of the vectors during the operation is immaterial, right?) and it is (0,0,-5) or (0,0,5). Is that right? The direction cosines are found by dividing the each component by the magnitude of the vector, right? So, using (0,0,-5), we get 0,0 and -1 for the direction cosines. Am I right?

I just need to know that my answers are correct, that's all! Please?
 
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Your answers are correct.
 
I agree with Kurtz. They are all correct. nice work
 

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