Linear Algebra: Dot Product and Orthogonality

Click For Summary
SUMMARY

The discussion centers on solving a linear algebra problem involving the dot product and orthogonality of vectors. The problem requires calculating the expression (3u - 8v) · (3u + 8v) given the magnitudes ||u|| = 5 and ||v|| = 7. The solution involves applying the linear properties of the dot product, which simplifies the computation significantly. The participant successfully solved the problem after receiving guidance on expanding the dot product.

PREREQUISITES
  • Understanding of vector magnitudes and notation
  • Familiarity with the properties of the dot product
  • Knowledge of linear algebra concepts, particularly vector operations
  • Ability to manipulate algebraic expressions involving vectors
NEXT STEPS
  • Study the properties of the dot product in detail
  • Learn about vector orthogonality and its implications in linear algebra
  • Explore examples of vector operations in linear algebra textbooks
  • Practice solving problems involving linear combinations of vectors
USEFUL FOR

Students studying linear algebra, educators teaching vector mathematics, and anyone looking to strengthen their understanding of dot products and vector operations.

mateomy
Messages
305
Reaction score
0
This is from my homework, I was moving along nicely until I hit this problem, (there's another just like it right after this). I can't find reference for solving this in the chapter I am looking at. The answer is in the back of the book….-2911. Can someone explain this to me?[tex] ||\mathbf{u}|| = 5\, and\: ||\mathbf{v}|| = 7; \,find\: (3\mathbf{u} - 8\mathbf{v}) \circ (3\mathbf{u} + 8\mathbf{v}).[/tex]I know that [itex]||\mathbf{u}||[/itex] is just the length of the vector, etc. I just don't know where to go from there.
 
Physics news on Phys.org
try expanding the dot product using its linear properties, should simplify a heap
 
You were right. Solved it first go after that. Thank you.
 

Similar threads

Write ∇u with covariant components and contravariant basis
  • · Replies 18 ·
Replies
18
Views
3K
Understanding Fixed Points in Hamiltonian Systems
  • · Replies 2 ·
Replies
2
Views
2K
Rate at which a bucket gets filled
  • · Replies 4 ·
Replies
4
Views
2K
Line Integral Notation wrt Scalar Value function
  • · Replies 3 ·
Replies
3
Views
2K
Orthogonal Projection Problems?
  • · Replies 5 ·
Replies
5
Views
2K
Linear combinations of 3 non-parallel vectors in 2D Euc.-space
  • · Replies 7 ·
Replies
7
Views
2K
[Linear Algebra] Sum & Direct Sum of Subspaces
  • · Replies 6 ·
Replies
6
Views
2K
Entropy (Information Theory Question)
  • · Replies 4 ·
Replies
4
Views
2K
Finding a complementary subspace ##U## | Linear Algebra
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Does Poisson's equation hold due to vector potential cancellation?
  • · Replies 3 ·
Replies
3
Views
1K