Vectors Math Help (solution check)

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SUMMARY

The discussion focuses on demonstrating that the vector identity ⃗ a ×(b⃗ ×c⃗ ) ≠ (a⃗ ×b⃗ )×c⃗ using specific vectors in three-dimensional space. Participants confirm the solution's validity and provide a method for verification through dot products. Specifically, the dot product of ⃗ a and ⃗ a × (b⃗ × c⃗ ) should yield zero, confirming perpendicularity. This approach is emphasized as a reliable technique for checking vector cross product identities.

PREREQUISITES
  • Understanding of vector cross products in three-dimensional space
  • Familiarity with the properties of dot products
  • Knowledge of vector notation and operations
  • Basic grasp of linear algebra concepts
NEXT STEPS
  • Study the properties of vector cross products in 3D space
  • Learn how to compute dot products and their geometric interpretations
  • Explore vector identities and their proofs in linear algebra
  • Investigate applications of vector mathematics in physics and engineering
USEFUL FOR

Students studying vector mathematics, educators teaching linear algebra, and anyone interested in understanding vector identities and their applications in physics.

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Homework Statement


Use three specific vectors in 3 space to show that ⃗ a ×(b⃗ ×c⃗ ) ≠ (a⃗ ×b⃗ )×c⃗

solution is in pdf...

Homework Equations

The Attempt at a Solution

 

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amy098yay said:

Homework Statement


Use three specific vectors in 3 space to show that ⃗ a ×(b⃗ ×c⃗ ) ≠ (a⃗ ×b⃗ )×c⃗

solution is in pdf...

Homework Equations

The Attempt at a Solution

Looks good now.
For future reference, you can check your answers. a x (b x c) should be perpendicular to both a and a x c. Just calculate the dot product of a and a x (b x c), and of (b x c) and a x (b x c). Each dot product should be zero. Same thing with the other triple product.
 
for sure, thank you so much for taking time out of your day to help me with this problem :)
 
You're welcome! Most of us helping out here like to do this...
 

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